id sid tid token lemma pos cord-026306-mkmrninv 1 1 key key NN cord-026306-mkmrninv 1 2 : : : cord-026306-mkmrninv 1 3 cord-026306-mkmrninv cord-026306-mkmrninv ADD cord-026306-mkmrninv 2 1 authors author NNS cord-026306-mkmrninv 2 2 : : : cord-026306-mkmrninv 2 3 Lepskiy Lepskiy NNP cord-026306-mkmrninv 2 4 , , , cord-026306-mkmrninv 2 5 Alexander Alexander NNP cord-026306-mkmrninv 2 6 ; ; : cord-026306-mkmrninv 2 7 Meshcheryakova Meshcheryakova NNP cord-026306-mkmrninv 2 8 , , , cord-026306-mkmrninv 3 1 Natalia Natalia NNP cord-026306-mkmrninv 3 2 title title NN cord-026306-mkmrninv 3 3 : : : cord-026306-mkmrninv 3 4 Belief Belief NNP cord-026306-mkmrninv 3 5 Functions function NNS cord-026306-mkmrninv 3 6 for for IN cord-026306-mkmrninv 3 7 the the DT cord-026306-mkmrninv 3 8 Importance Importance NNP cord-026306-mkmrninv 3 9 Assessment Assessment NNP cord-026306-mkmrninv 3 10 in in IN cord-026306-mkmrninv 3 11 Multiplex Multiplex NNP cord-026306-mkmrninv 3 12 Networks Networks NNP cord-026306-mkmrninv 3 13 date date NN cord-026306-mkmrninv 3 14 : : : cord-026306-mkmrninv 3 15 2020 2020 CD cord-026306-mkmrninv 3 16 - - HYPH cord-026306-mkmrninv 3 17 05 05 CD cord-026306-mkmrninv 3 18 - - SYM cord-026306-mkmrninv 3 19 15 15 CD cord-026306-mkmrninv 3 20 journal journal NN cord-026306-mkmrninv 3 21 : : : cord-026306-mkmrninv 3 22 Information Information NNP cord-026306-mkmrninv 3 23 Processing Processing NNP cord-026306-mkmrninv 3 24 and and CC cord-026306-mkmrninv 3 25 Management Management NNP cord-026306-mkmrninv 3 26 of of IN cord-026306-mkmrninv 3 27 Uncertainty Uncertainty NNP cord-026306-mkmrninv 3 28 in in IN cord-026306-mkmrninv 3 29 Knowledge Knowledge NNP cord-026306-mkmrninv 3 30 - - HYPH cord-026306-mkmrninv 3 31 Based Based NNP cord-026306-mkmrninv 3 32 Systems Systems NNP cord-026306-mkmrninv 3 33 DOI DOI NNP cord-026306-mkmrninv 3 34 : : : cord-026306-mkmrninv 3 35 10.1007/978 10.1007/978 CD cord-026306-mkmrninv 3 36 - - HYPH cord-026306-mkmrninv 3 37 3 3 CD cord-026306-mkmrninv 3 38 - - HYPH cord-026306-mkmrninv 3 39 030 030 CD cord-026306-mkmrninv 3 40 - - HYPH cord-026306-mkmrninv 3 41 50143 50143 CD cord-026306-mkmrninv 3 42 - - SYM cord-026306-mkmrninv 3 43 3_22 3_22 CD cord-026306-mkmrninv 3 44 sha sha NNP cord-026306-mkmrninv 3 45 : : : cord-026306-mkmrninv 4 1 61d261015f8746d224ec9f96f893ffafd1b8372c 61d261015f8746d224ec9f96f893ffafd1b8372c CD cord-026306-mkmrninv 4 2 doc_id doc_id CD cord-026306-mkmrninv 4 3 : : : cord-026306-mkmrninv 5 1 26306 26306 CD cord-026306-mkmrninv 5 2 cord_uid cord_uid NNS cord-026306-mkmrninv 5 3 : : : cord-026306-mkmrninv 5 4 mkmrninv mkmrninv NN cord-026306-mkmrninv 6 1 We -PRON- PRP cord-026306-mkmrninv 6 2 apply apply VBP cord-026306-mkmrninv 6 3 Dempster Dempster NNP cord-026306-mkmrninv 6 4 - - HYPH cord-026306-mkmrninv 6 5 Shafer Shafer NNP cord-026306-mkmrninv 6 6 theory theory NN cord-026306-mkmrninv 6 7 in in IN cord-026306-mkmrninv 6 8 order order NN cord-026306-mkmrninv 6 9 to to TO cord-026306-mkmrninv 6 10 reveal reveal VB cord-026306-mkmrninv 6 11 important important JJ cord-026306-mkmrninv 6 12 elements element NNS cord-026306-mkmrninv 6 13 in in IN cord-026306-mkmrninv 6 14 undirected undirected JJ cord-026306-mkmrninv 6 15 weighted weighted JJ cord-026306-mkmrninv 6 16 networks network NNS cord-026306-mkmrninv 6 17 . . . cord-026306-mkmrninv 7 1 We -PRON- PRP cord-026306-mkmrninv 7 2 estimate estimate VBP cord-026306-mkmrninv 7 3 cooperation cooperation NN cord-026306-mkmrninv 7 4 of of IN cord-026306-mkmrninv 7 5 each each DT cord-026306-mkmrninv 7 6 node node NN cord-026306-mkmrninv 7 7 with with IN cord-026306-mkmrninv 7 8 different different JJ cord-026306-mkmrninv 7 9 groups group NNS cord-026306-mkmrninv 7 10 of of IN cord-026306-mkmrninv 7 11 vertices vertex NNS cord-026306-mkmrninv 7 12 that that WDT cord-026306-mkmrninv 7 13 surround surround VBP cord-026306-mkmrninv 7 14 it -PRON- PRP cord-026306-mkmrninv 7 15 via via IN cord-026306-mkmrninv 7 16 construction construction NN cord-026306-mkmrninv 7 17 of of IN cord-026306-mkmrninv 7 18 belief belief NN cord-026306-mkmrninv 7 19 functions function NNS cord-026306-mkmrninv 7 20 . . . cord-026306-mkmrninv 8 1 The the DT cord-026306-mkmrninv 8 2 obtained obtain VBN cord-026306-mkmrninv 8 3 intensities intensity NNS cord-026306-mkmrninv 8 4 of of IN cord-026306-mkmrninv 8 5 cooperation cooperation NN cord-026306-mkmrninv 8 6 are be VBP cord-026306-mkmrninv 8 7 further further RB cord-026306-mkmrninv 8 8 redistributed redistribute VBN cord-026306-mkmrninv 8 9 over over IN cord-026306-mkmrninv 8 10 all all DT cord-026306-mkmrninv 8 11 elements element NNS cord-026306-mkmrninv 8 12 of of IN cord-026306-mkmrninv 8 13 a a DT cord-026306-mkmrninv 8 14 particular particular JJ cord-026306-mkmrninv 8 15 group group NN cord-026306-mkmrninv 8 16 of of IN cord-026306-mkmrninv 8 17 nodes node NNS cord-026306-mkmrninv 8 18 that that WDT cord-026306-mkmrninv 8 19 results result VBZ cord-026306-mkmrninv 8 20 in in IN cord-026306-mkmrninv 8 21 pignistic pignistic JJ cord-026306-mkmrninv 8 22 probabilities probability NNS cord-026306-mkmrninv 8 23 of of IN cord-026306-mkmrninv 8 24 node node NN cord-026306-mkmrninv 8 25 - - HYPH cord-026306-mkmrninv 8 26 to to IN cord-026306-mkmrninv 8 27 - - HYPH cord-026306-mkmrninv 8 28 node node NN cord-026306-mkmrninv 8 29 interactions interaction NNS cord-026306-mkmrninv 8 30 . . . cord-026306-mkmrninv 9 1 Finally finally RB cord-026306-mkmrninv 9 2 , , , cord-026306-mkmrninv 9 3 pairwise pairwise JJ cord-026306-mkmrninv 9 4 interactions interaction NNS cord-026306-mkmrninv 9 5 can can MD cord-026306-mkmrninv 9 6 be be VB cord-026306-mkmrninv 9 7 aggregated aggregate VBN cord-026306-mkmrninv 9 8 into into IN cord-026306-mkmrninv 9 9 the the DT cord-026306-mkmrninv 9 10 centrality centrality NN cord-026306-mkmrninv 9 11 vector vector NN cord-026306-mkmrninv 9 12 that that WDT cord-026306-mkmrninv 9 13 ranks rank VBZ cord-026306-mkmrninv 9 14 nodes node NNS cord-026306-mkmrninv 9 15 with with IN cord-026306-mkmrninv 9 16 respect respect NN cord-026306-mkmrninv 9 17 to to IN cord-026306-mkmrninv 9 18 derived derived JJ cord-026306-mkmrninv 9 19 values value NNS cord-026306-mkmrninv 9 20 . . . cord-026306-mkmrninv 10 1 We -PRON- PRP cord-026306-mkmrninv 10 2 also also RB cord-026306-mkmrninv 10 3 adapt adapt VBP cord-026306-mkmrninv 10 4 the the DT cord-026306-mkmrninv 10 5 proposed propose VBN cord-026306-mkmrninv 10 6 model model NN cord-026306-mkmrninv 10 7 to to IN cord-026306-mkmrninv 10 8 multiplex multiplex JJ cord-026306-mkmrninv 10 9 networks network NNS cord-026306-mkmrninv 10 10 . . . cord-026306-mkmrninv 11 1 In in IN cord-026306-mkmrninv 11 2 this this DT cord-026306-mkmrninv 11 3 type type NN cord-026306-mkmrninv 11 4 of of IN cord-026306-mkmrninv 11 5 networks network NNS cord-026306-mkmrninv 11 6 nodes node NNS cord-026306-mkmrninv 11 7 can can MD cord-026306-mkmrninv 11 8 be be VB cord-026306-mkmrninv 11 9 differently differently RB cord-026306-mkmrninv 11 10 connected connect VBN cord-026306-mkmrninv 11 11 with with IN cord-026306-mkmrninv 11 12 each each DT cord-026306-mkmrninv 11 13 other other JJ cord-026306-mkmrninv 11 14 on on IN cord-026306-mkmrninv 11 15 several several JJ cord-026306-mkmrninv 11 16 levels level NNS cord-026306-mkmrninv 11 17 of of IN cord-026306-mkmrninv 11 18 interaction interaction NN cord-026306-mkmrninv 11 19 . . . cord-026306-mkmrninv 12 1 Various various JJ cord-026306-mkmrninv 12 2 combination combination NN cord-026306-mkmrninv 12 3 rules rule NNS cord-026306-mkmrninv 12 4 help help VBP cord-026306-mkmrninv 12 5 to to TO cord-026306-mkmrninv 12 6 analyze analyze VB cord-026306-mkmrninv 12 7 such such JJ cord-026306-mkmrninv 12 8 systems system NNS cord-026306-mkmrninv 12 9 as as IN cord-026306-mkmrninv 12 10 a a DT cord-026306-mkmrninv 12 11 single single JJ cord-026306-mkmrninv 12 12 entity entity NN cord-026306-mkmrninv 12 13 , , , cord-026306-mkmrninv 12 14 that that WDT cord-026306-mkmrninv 12 15 has have VBZ cord-026306-mkmrninv 12 16 many many JJ cord-026306-mkmrninv 12 17 advantages advantage NNS cord-026306-mkmrninv 12 18 in in IN cord-026306-mkmrninv 12 19 the the DT cord-026306-mkmrninv 12 20 study study NN cord-026306-mkmrninv 12 21 of of IN cord-026306-mkmrninv 12 22 complex complex JJ cord-026306-mkmrninv 12 23 systems system NNS cord-026306-mkmrninv 12 24 . . . cord-026306-mkmrninv 13 1 In in IN cord-026306-mkmrninv 13 2 particular particular JJ cord-026306-mkmrninv 13 3 , , , cord-026306-mkmrninv 13 4 Dempster Dempster NNP cord-026306-mkmrninv 13 5 rule rule NN cord-026306-mkmrninv 13 6 takes take VBZ cord-026306-mkmrninv 13 7 into into IN cord-026306-mkmrninv 13 8 account account NN cord-026306-mkmrninv 13 9 the the DT cord-026306-mkmrninv 13 10 inconsistency inconsistency NN cord-026306-mkmrninv 13 11 in in IN cord-026306-mkmrninv 13 12 initial initial JJ cord-026306-mkmrninv 13 13 data datum NNS cord-026306-mkmrninv 13 14 that that WDT cord-026306-mkmrninv 13 15 has have VBZ cord-026306-mkmrninv 13 16 an an DT cord-026306-mkmrninv 13 17 impact impact NN cord-026306-mkmrninv 13 18 on on IN cord-026306-mkmrninv 13 19 the the DT cord-026306-mkmrninv 13 20 final final JJ cord-026306-mkmrninv 13 21 centrality centrality NN cord-026306-mkmrninv 13 22 ranking ranking NN cord-026306-mkmrninv 13 23 . . . cord-026306-mkmrninv 14 1 We -PRON- PRP cord-026306-mkmrninv 14 2 also also RB cord-026306-mkmrninv 14 3 provide provide VBP cord-026306-mkmrninv 14 4 a a DT cord-026306-mkmrninv 14 5 numerical numerical JJ cord-026306-mkmrninv 14 6 example example NN cord-026306-mkmrninv 14 7 that that WDT cord-026306-mkmrninv 14 8 illustrates illustrate VBZ cord-026306-mkmrninv 14 9 the the DT cord-026306-mkmrninv 14 10 distinctive distinctive JJ cord-026306-mkmrninv 14 11 features feature NNS cord-026306-mkmrninv 14 12 of of IN cord-026306-mkmrninv 14 13 the the DT cord-026306-mkmrninv 14 14 proposed propose VBN cord-026306-mkmrninv 14 15 model model NN cord-026306-mkmrninv 14 16 . . . cord-026306-mkmrninv 15 1 Additionally additionally RB cord-026306-mkmrninv 15 2 , , , cord-026306-mkmrninv 15 3 we -PRON- PRP cord-026306-mkmrninv 15 4 establish establish VBP cord-026306-mkmrninv 15 5 analytical analytical JJ cord-026306-mkmrninv 15 6 relations relation NNS cord-026306-mkmrninv 15 7 between between IN cord-026306-mkmrninv 15 8 a a DT cord-026306-mkmrninv 15 9 proposed propose VBN cord-026306-mkmrninv 15 10 measure measure NN cord-026306-mkmrninv 15 11 and and CC cord-026306-mkmrninv 15 12 classical classical JJ cord-026306-mkmrninv 15 13 centrality centrality NN cord-026306-mkmrninv 15 14 measures measure NNS cord-026306-mkmrninv 15 15 for for IN cord-026306-mkmrninv 15 16 particular particular JJ cord-026306-mkmrninv 15 17 graph graph NN cord-026306-mkmrninv 15 18 configurations configuration NNS cord-026306-mkmrninv 15 19 . . . cord-026306-mkmrninv 16 1 Dempster Dempster NNP cord-026306-mkmrninv 16 2 - - HYPH cord-026306-mkmrninv 16 3 Shafer Shafer NNP cord-026306-mkmrninv 16 4 theory theory NN cord-026306-mkmrninv 16 5 of of IN cord-026306-mkmrninv 16 6 belief belief NN cord-026306-mkmrninv 16 7 functions function NNS cord-026306-mkmrninv 16 8 [ [ -LRB- cord-026306-mkmrninv 16 9 1 1 CD cord-026306-mkmrninv 16 10 , , , cord-026306-mkmrninv 16 11 2 2 CD cord-026306-mkmrninv 16 12 ] ] -RRB- cord-026306-mkmrninv 16 13 is be VBZ cord-026306-mkmrninv 16 14 a a DT cord-026306-mkmrninv 16 15 widely widely RB cord-026306-mkmrninv 16 16 used use VBN cord-026306-mkmrninv 16 17 tool tool NN cord-026306-mkmrninv 16 18 to to TO cord-026306-mkmrninv 16 19 measure measure VB cord-026306-mkmrninv 16 20 belief belief NN cord-026306-mkmrninv 16 21 or or CC cord-026306-mkmrninv 16 22 conflict conflict NN cord-026306-mkmrninv 16 23 between between IN cord-026306-mkmrninv 16 24 elements element NNS cord-026306-mkmrninv 16 25 in in IN cord-026306-mkmrninv 16 26 a a DT cord-026306-mkmrninv 16 27 considered consider VBN cord-026306-mkmrninv 16 28 system system NN cord-026306-mkmrninv 16 29 [ [ -LRB- cord-026306-mkmrninv 16 30 1 1 CD cord-026306-mkmrninv 16 31 , , , cord-026306-mkmrninv 16 32 2 2 CD cord-026306-mkmrninv 16 33 ] ] -RRB- cord-026306-mkmrninv 16 34 . . . cord-026306-mkmrninv 17 1 Recently recently RB cord-026306-mkmrninv 17 2 it -PRON- PRP cord-026306-mkmrninv 17 3 has have VBZ cord-026306-mkmrninv 17 4 also also RB cord-026306-mkmrninv 17 5 found find VBN cord-026306-mkmrninv 17 6 use use NN cord-026306-mkmrninv 17 7 in in IN cord-026306-mkmrninv 17 8 the the DT cord-026306-mkmrninv 17 9 field field NN cord-026306-mkmrninv 17 10 of of IN cord-026306-mkmrninv 17 11 social social JJ cord-026306-mkmrninv 17 12 network network NN cord-026306-mkmrninv 17 13 analysis analysis NN cord-026306-mkmrninv 17 14 [ [ -LRB- cord-026306-mkmrninv 17 15 3 3 CD cord-026306-mkmrninv 17 16 ] ] -RRB- cord-026306-mkmrninv 17 17 . . . cord-026306-mkmrninv 18 1 Social social JJ cord-026306-mkmrninv 18 2 networks network NNS cord-026306-mkmrninv 18 3 represent represent VBP cord-026306-mkmrninv 18 4 interactions interaction NNS cord-026306-mkmrninv 18 5 that that WDT cord-026306-mkmrninv 18 6 are be VBP cord-026306-mkmrninv 18 7 met meet VBN cord-026306-mkmrninv 18 8 between between IN cord-026306-mkmrninv 18 9 people people NNS cord-026306-mkmrninv 18 10 , , , cord-026306-mkmrninv 18 11 countries country NNS cord-026306-mkmrninv 18 12 , , , cord-026306-mkmrninv 18 13 in in IN cord-026306-mkmrninv 18 14 transportation transportation NN cord-026306-mkmrninv 18 15 systems system NNS cord-026306-mkmrninv 18 16 , , , cord-026306-mkmrninv 18 17 etc etc FW cord-026306-mkmrninv 18 18 . . . cord-026306-mkmrninv 19 1 One one CD cord-026306-mkmrninv 19 2 of of IN cord-026306-mkmrninv 19 3 the the DT cord-026306-mkmrninv 19 4 core core NN cord-026306-mkmrninv 19 5 problems problem NNS cord-026306-mkmrninv 19 6 in in IN cord-026306-mkmrninv 19 7 network network NN cord-026306-mkmrninv 19 8 science science NN cord-026306-mkmrninv 19 9 is be VBZ cord-026306-mkmrninv 19 10 the the DT cord-026306-mkmrninv 19 11 detection detection NN cord-026306-mkmrninv 19 12 of of IN cord-026306-mkmrninv 19 13 central central JJ cord-026306-mkmrninv 19 14 elements element NNS cord-026306-mkmrninv 19 15 . . . cord-026306-mkmrninv 20 1 In in IN cord-026306-mkmrninv 20 2 [ [ -LRB- cord-026306-mkmrninv 20 3 4 4 CD cord-026306-mkmrninv 20 4 ] ] -RRB- cord-026306-mkmrninv 20 5 a a DT cord-026306-mkmrninv 20 6 modified modify VBN cord-026306-mkmrninv 20 7 evidential evidential JJ cord-026306-mkmrninv 20 8 centrality centrality NN cord-026306-mkmrninv 20 9 and and CC cord-026306-mkmrninv 20 10 evidential evidential JJ cord-026306-mkmrninv 20 11 semi semi JJ cord-026306-mkmrninv 20 12 - - JJ cord-026306-mkmrninv 20 13 local local JJ cord-026306-mkmrninv 20 14 centrality centrality NN cord-026306-mkmrninv 20 15 in in IN cord-026306-mkmrninv 20 16 weighted weighted JJ cord-026306-mkmrninv 20 17 network network NN cord-026306-mkmrninv 20 18 are be VBP cord-026306-mkmrninv 20 19 proposed propose VBN cord-026306-mkmrninv 20 20 . . . cord-026306-mkmrninv 21 1 The the DT cord-026306-mkmrninv 21 2 measures measure NNS cord-026306-mkmrninv 21 3 use use VBP cord-026306-mkmrninv 21 4 the the DT cord-026306-mkmrninv 21 5 combination combination NN cord-026306-mkmrninv 21 6 of of IN cord-026306-mkmrninv 21 7 " " `` cord-026306-mkmrninv 21 8 high high JJ cord-026306-mkmrninv 21 9 " " '' cord-026306-mkmrninv 21 10 , , , cord-026306-mkmrninv 21 11 " " `` cord-026306-mkmrninv 21 12 low low JJ cord-026306-mkmrninv 21 13 " " '' cord-026306-mkmrninv 21 14 and and CC cord-026306-mkmrninv 21 15 " " '' cord-026306-mkmrninv 21 16 ( ( -LRB- cord-026306-mkmrninv 21 17 high high JJ cord-026306-mkmrninv 21 18 , , , cord-026306-mkmrninv 21 19 low low JJ cord-026306-mkmrninv 21 20 ) ) -RRB- cord-026306-mkmrninv 21 21 " " `` cord-026306-mkmrninv 21 22 probabilities probability NNS cord-026306-mkmrninv 21 23 of of IN cord-026306-mkmrninv 21 24 the the DT cord-026306-mkmrninv 21 25 influence influence NN cord-026306-mkmrninv 21 26 based base VBN cord-026306-mkmrninv 21 27 on on IN cord-026306-mkmrninv 21 28 weighted weighted JJ cord-026306-mkmrninv 21 29 and and CC cord-026306-mkmrninv 21 30 unweighted unweighted JJ cord-026306-mkmrninv 21 31 degrees degree NNS cord-026306-mkmrninv 21 32 of of IN cord-026306-mkmrninv 21 33 nodes node NNS cord-026306-mkmrninv 21 34 via via IN cord-026306-mkmrninv 21 35 Dempster Dempster NNP cord-026306-mkmrninv 21 36 's 's POS cord-026306-mkmrninv 21 37 rule rule NN cord-026306-mkmrninv 21 38 . . . cord-026306-mkmrninv 22 1 In in IN cord-026306-mkmrninv 22 2 [ [ -LRB- cord-026306-mkmrninv 22 3 5 5 CD cord-026306-mkmrninv 22 4 ] ] -RRB- cord-026306-mkmrninv 22 5 the the DT cord-026306-mkmrninv 22 6 same same JJ cord-026306-mkmrninv 22 7 rule rule NN cord-026306-mkmrninv 22 8 is be VBZ cord-026306-mkmrninv 22 9 applied apply VBN cord-026306-mkmrninv 22 10 in in IN cord-026306-mkmrninv 22 11 order order NN cord-026306-mkmrninv 22 12 to to TO cord-026306-mkmrninv 22 13 combine combine VB cord-026306-mkmrninv 22 14 different different JJ cord-026306-mkmrninv 22 15 node node NN cord-026306-mkmrninv 22 16 - - HYPH cord-026306-mkmrninv 22 17 to to IN cord-026306-mkmrninv 22 18 - - HYPH cord-026306-mkmrninv 22 19 node node NN cord-026306-mkmrninv 22 20 interactions interaction NNS cord-026306-mkmrninv 22 21 in in IN cord-026306-mkmrninv 22 22 a a DT cord-026306-mkmrninv 22 23 network network NN cord-026306-mkmrninv 22 24 . . . cord-026306-mkmrninv 23 1 The the DT cord-026306-mkmrninv 23 2 proposed propose VBN cord-026306-mkmrninv 23 3 measures measure NNS cord-026306-mkmrninv 23 4 that that WDT cord-026306-mkmrninv 23 5 are be VBP cord-026306-mkmrninv 23 6 able able JJ cord-026306-mkmrninv 23 7 to to TO cord-026306-mkmrninv 23 8 detect detect VB cord-026306-mkmrninv 23 9 social social JJ cord-026306-mkmrninv 23 10 influencers influencer NNS cord-026306-mkmrninv 23 11 were be VBD cord-026306-mkmrninv 23 12 applied apply VBN cord-026306-mkmrninv 23 13 to to IN cord-026306-mkmrninv 23 14 Twitter Twitter NNP cord-026306-mkmrninv 23 15 data datum NNS cord-026306-mkmrninv 23 16 . . . cord-026306-mkmrninv 24 1 The the DT cord-026306-mkmrninv 24 2 theory theory NN cord-026306-mkmrninv 24 3 of of IN cord-026306-mkmrninv 24 4 belief belief NN cord-026306-mkmrninv 24 5 functions function NNS cord-026306-mkmrninv 24 6 can can MD cord-026306-mkmrninv 24 7 be be VB cord-026306-mkmrninv 24 8 also also RB cord-026306-mkmrninv 24 9 adapted adapt VBN cord-026306-mkmrninv 24 10 to to IN cord-026306-mkmrninv 24 11 the the DT cord-026306-mkmrninv 24 12 problem problem NN cord-026306-mkmrninv 24 13 of of IN cord-026306-mkmrninv 24 14 community community NN cord-026306-mkmrninv 24 15 detection detection NN cord-026306-mkmrninv 24 16 , , , cord-026306-mkmrninv 24 17 i.e. i.e. FW cord-026306-mkmrninv 24 18 the the DT cord-026306-mkmrninv 24 19 partition partition NN cord-026306-mkmrninv 24 20 of of IN cord-026306-mkmrninv 24 21 nodes node NNS cord-026306-mkmrninv 24 22 into into IN cord-026306-mkmrninv 24 23 tightly tightly RB cord-026306-mkmrninv 24 24 connected connected JJ cord-026306-mkmrninv 24 25 groups group NNS cord-026306-mkmrninv 24 26 . . . cord-026306-mkmrninv 25 1 For for IN cord-026306-mkmrninv 25 2 instance instance NN cord-026306-mkmrninv 25 3 , , , cord-026306-mkmrninv 25 4 in in IN cord-026306-mkmrninv 25 5 [ [ -LRB- cord-026306-mkmrninv 25 6 6 6 CD cord-026306-mkmrninv 25 7 ] ] -RRB- cord-026306-mkmrninv 25 8 the the DT cord-026306-mkmrninv 25 9 author author NN cord-026306-mkmrninv 25 10 proposed propose VBD cord-026306-mkmrninv 25 11 a a DT cord-026306-mkmrninv 25 12 novel novel JJ cord-026306-mkmrninv 25 13 method method NN cord-026306-mkmrninv 25 14 based base VBN cord-026306-mkmrninv 25 15 on on IN cord-026306-mkmrninv 25 16 local local JJ cord-026306-mkmrninv 25 17 density density NN cord-026306-mkmrninv 25 18 measures measure NNS cord-026306-mkmrninv 25 19 assigned assign VBN cord-026306-mkmrninv 25 20 to to IN cord-026306-mkmrninv 25 21 each each DT cord-026306-mkmrninv 25 22 node node NN cord-026306-mkmrninv 25 23 that that WDT cord-026306-mkmrninv 25 24 are be VBP cord-026306-mkmrninv 25 25 further further RB cord-026306-mkmrninv 25 26 used use VBN cord-026306-mkmrninv 25 27 for for IN cord-026306-mkmrninv 25 28 the the DT cord-026306-mkmrninv 25 29 detection detection NN cord-026306-mkmrninv 25 30 density density NN cord-026306-mkmrninv 25 31 peaks peak NNS cord-026306-mkmrninv 25 32 in in IN cord-026306-mkmrninv 25 33 a a DT cord-026306-mkmrninv 25 34 graph graph NN cord-026306-mkmrninv 25 35 . . . cord-026306-mkmrninv 26 1 In in IN cord-026306-mkmrninv 26 2 the the DT cord-026306-mkmrninv 26 3 frame frame NN cord-026306-mkmrninv 26 4 of of IN cord-026306-mkmrninv 26 5 the the DT cord-026306-mkmrninv 26 6 recent recent JJ cord-026306-mkmrninv 26 7 work work NN cord-026306-mkmrninv 26 8 we -PRON- PRP cord-026306-mkmrninv 26 9 mostly mostly RB cord-026306-mkmrninv 26 10 focus focus VBP cord-026306-mkmrninv 26 11 on on IN cord-026306-mkmrninv 26 12 the the DT cord-026306-mkmrninv 26 13 problem problem NN cord-026306-mkmrninv 26 14 of of IN cord-026306-mkmrninv 26 15 the the DT cord-026306-mkmrninv 26 16 detection detection NN cord-026306-mkmrninv 26 17 of of IN cord-026306-mkmrninv 26 18 the the DT cord-026306-mkmrninv 26 19 most most RBS cord-026306-mkmrninv 26 20 influential influential JJ cord-026306-mkmrninv 26 21 as as RB cord-026306-mkmrninv 26 22 well well RB cord-026306-mkmrninv 26 23 as as IN cord-026306-mkmrninv 26 24 the the DT cord-026306-mkmrninv 26 25 most most RBS cord-026306-mkmrninv 26 26 affected affect VBN cord-026306-mkmrninv 26 27 elements element NNS cord-026306-mkmrninv 26 28 in in IN cord-026306-mkmrninv 26 29 networks network NNS cord-026306-mkmrninv 26 30 . . . cord-026306-mkmrninv 27 1 The the DT cord-026306-mkmrninv 27 2 knowledge knowledge NN cord-026306-mkmrninv 27 3 about about IN cord-026306-mkmrninv 27 4 the the DT cord-026306-mkmrninv 27 5 position position NN cord-026306-mkmrninv 27 6 of of IN cord-026306-mkmrninv 27 7 nodes node NNS cord-026306-mkmrninv 27 8 plays play VBZ cord-026306-mkmrninv 27 9 a a DT cord-026306-mkmrninv 27 10 significant significant JJ cord-026306-mkmrninv 27 11 role role NN cord-026306-mkmrninv 27 12 in in IN cord-026306-mkmrninv 27 13 understanding understanding NN cord-026306-mkmrninv 27 14 of of IN cord-026306-mkmrninv 27 15 structural structural JJ cord-026306-mkmrninv 27 16 properties property NNS cord-026306-mkmrninv 27 17 of of IN cord-026306-mkmrninv 27 18 complex complex JJ cord-026306-mkmrninv 27 19 systems system NNS cord-026306-mkmrninv 27 20 . . . cord-026306-mkmrninv 28 1 There there EX cord-026306-mkmrninv 28 2 exist exist VBP cord-026306-mkmrninv 28 3 several several JJ cord-026306-mkmrninv 28 4 networking networking NN cord-026306-mkmrninv 28 5 approaches approach NNS cord-026306-mkmrninv 28 6 that that WDT cord-026306-mkmrninv 28 7 aim aim VBP cord-026306-mkmrninv 28 8 to to TO cord-026306-mkmrninv 28 9 assess assess VB cord-026306-mkmrninv 28 10 the the DT cord-026306-mkmrninv 28 11 importance importance NN cord-026306-mkmrninv 28 12 of of IN cord-026306-mkmrninv 28 13 nodes node NNS cord-026306-mkmrninv 28 14 in in IN cord-026306-mkmrninv 28 15 graphs graph NNS cord-026306-mkmrninv 28 16 . . . cord-026306-mkmrninv 29 1 The the DT cord-026306-mkmrninv 29 2 first first JJ cord-026306-mkmrninv 29 3 class class NN cord-026306-mkmrninv 29 4 of of IN cord-026306-mkmrninv 29 5 the the DT cord-026306-mkmrninv 29 6 methods method NNS cord-026306-mkmrninv 29 7 refers refer VBZ cord-026306-mkmrninv 29 8 to to IN cord-026306-mkmrninv 29 9 classical classical JJ cord-026306-mkmrninv 29 10 centrality centrality NN cord-026306-mkmrninv 29 11 measures measure NNS cord-026306-mkmrninv 29 12 [ [ -LRB- cord-026306-mkmrninv 29 13 7 7 CD cord-026306-mkmrninv 29 14 ] ] -RRB- cord-026306-mkmrninv 29 15 . . . cord-026306-mkmrninv 30 1 It -PRON- PRP cord-026306-mkmrninv 30 2 includes include VBZ cord-026306-mkmrninv 30 3 degree degree NN cord-026306-mkmrninv 30 4 centrality centrality NN cord-026306-mkmrninv 30 5 measure measure NN cord-026306-mkmrninv 30 6 that that WDT cord-026306-mkmrninv 30 7 prioritizes prioritize VBZ cord-026306-mkmrninv 30 8 over over IN cord-026306-mkmrninv 30 9 nodes node NNS cord-026306-mkmrninv 30 10 with with IN cord-026306-mkmrninv 30 11 the the DT cord-026306-mkmrninv 30 12 largest large JJS cord-026306-mkmrninv 30 13 number number NN cord-026306-mkmrninv 30 14 of of IN cord-026306-mkmrninv 30 15 neighbors neighbor NNS cord-026306-mkmrninv 30 16 or or CC cord-026306-mkmrninv 30 17 with with IN cord-026306-mkmrninv 30 18 the the DT cord-026306-mkmrninv 30 19 largest large JJS cord-026306-mkmrninv 30 20 sum sum NN cord-026306-mkmrninv 30 21 of of IN cord-026306-mkmrninv 30 22 incoming incoming JJ cord-026306-mkmrninv 30 23 / / SYM cord-026306-mkmrninv 30 24 outcoming outcoming JJ cord-026306-mkmrninv 30 25 weights weight NNS cord-026306-mkmrninv 30 26 . . . cord-026306-mkmrninv 31 1 The the DT cord-026306-mkmrninv 31 2 eigenvector eigenvector NN cord-026306-mkmrninv 31 3 group group NN cord-026306-mkmrninv 31 4 of of IN cord-026306-mkmrninv 31 5 centralities centrality NNS cord-026306-mkmrninv 31 6 , , , cord-026306-mkmrninv 31 7 that that WDT cord-026306-mkmrninv 31 8 includes include VBZ cord-026306-mkmrninv 31 9 eigenvector eigenvector NN cord-026306-mkmrninv 31 10 centrality centrality NN cord-026306-mkmrninv 31 11 itself -PRON- PRP cord-026306-mkmrninv 31 12 , , , cord-026306-mkmrninv 31 13 Bonacich Bonacich NNP cord-026306-mkmrninv 31 14 , , , cord-026306-mkmrninv 31 15 PageRank PageRank NNP cord-026306-mkmrninv 31 16 , , , cord-026306-mkmrninv 31 17 Katz Katz NNP cord-026306-mkmrninv 31 18 , , , cord-026306-mkmrninv 31 19 Hubs Hubs NNP cord-026306-mkmrninv 31 20 and and CC cord-026306-mkmrninv 31 21 Authorities Authorities NNPS cord-026306-mkmrninv 31 22 , , , cord-026306-mkmrninv 31 23 Alpha alpha NN cord-026306-mkmrninv 31 24 centrality centrality NN cord-026306-mkmrninv 31 25 , , , cord-026306-mkmrninv 31 26 etc etc FW cord-026306-mkmrninv 31 27 . . FW cord-026306-mkmrninv 31 28 , , , cord-026306-mkmrninv 31 29 takes take VBZ cord-026306-mkmrninv 31 30 into into IN cord-026306-mkmrninv 31 31 account account NN cord-026306-mkmrninv 31 32 the the DT cord-026306-mkmrninv 31 33 importance importance NN cord-026306-mkmrninv 31 34 of of IN cord-026306-mkmrninv 31 35 neighbors neighbor NNS cord-026306-mkmrninv 31 36 of of IN cord-026306-mkmrninv 31 37 a a DT cord-026306-mkmrninv 31 38 node node NN cord-026306-mkmrninv 31 39 , , , cord-026306-mkmrninv 31 40 i.e. i.e. FW cord-026306-mkmrninv 31 41 the the DT cord-026306-mkmrninv 31 42 centrality centrality NN cord-026306-mkmrninv 31 43 of of IN cord-026306-mkmrninv 31 44 a a DT cord-026306-mkmrninv 31 45 vertex vertex NN cord-026306-mkmrninv 31 46 depends depend VBZ cord-026306-mkmrninv 31 47 on on IN cord-026306-mkmrninv 31 48 centralities centrality NNS cord-026306-mkmrninv 31 49 of of IN cord-026306-mkmrninv 31 50 the the DT cord-026306-mkmrninv 31 51 adjacent adjacent JJ cord-026306-mkmrninv 31 52 nodes node NNS cord-026306-mkmrninv 31 53 [ [ -LRB- cord-026306-mkmrninv 31 54 8 8 CD cord-026306-mkmrninv 31 55 ] ] -RRB- cord-026306-mkmrninv 31 56 [ [ -LRB- cord-026306-mkmrninv 31 57 9 9 CD cord-026306-mkmrninv 31 58 ] ] -RRB- cord-026306-mkmrninv 31 59 [ [ -LRB- cord-026306-mkmrninv 31 60 10 10 CD cord-026306-mkmrninv 31 61 ] ] -RRB- cord-026306-mkmrninv 31 62 [ [ -LRB- cord-026306-mkmrninv 31 63 11 11 CD cord-026306-mkmrninv 31 64 ] ] -RRB- cord-026306-mkmrninv 31 65 [ [ -LRB- cord-026306-mkmrninv 31 66 12 12 CD cord-026306-mkmrninv 31 67 ] ] -RRB- cord-026306-mkmrninv 31 68 . . . cord-026306-mkmrninv 32 1 Closeness closeness NN cord-026306-mkmrninv 32 2 and and CC cord-026306-mkmrninv 32 3 betweenness betweenness NN cord-026306-mkmrninv 32 4 centralities centrality NNS cord-026306-mkmrninv 32 5 consider consider VBP cord-026306-mkmrninv 32 6 the the DT cord-026306-mkmrninv 32 7 distance distance NN cord-026306-mkmrninv 32 8 between between IN cord-026306-mkmrninv 32 9 nodes node NNS cord-026306-mkmrninv 32 10 and and CC cord-026306-mkmrninv 32 11 the the DT cord-026306-mkmrninv 32 12 number number NN cord-026306-mkmrninv 32 13 of of IN cord-026306-mkmrninv 32 14 the the DT cord-026306-mkmrninv 32 15 shortest short JJS cord-026306-mkmrninv 32 16 paths path NNS cord-026306-mkmrninv 32 17 that that WDT cord-026306-mkmrninv 32 18 go go VBP cord-026306-mkmrninv 32 19 through through IN cord-026306-mkmrninv 32 20 nodes node NNS cord-026306-mkmrninv 32 21 in in IN cord-026306-mkmrninv 32 22 a a DT cord-026306-mkmrninv 32 23 network network NN cord-026306-mkmrninv 32 24 [ [ -LRB- cord-026306-mkmrninv 32 25 13 13 CD cord-026306-mkmrninv 32 26 , , , cord-026306-mkmrninv 32 27 14 14 CD cord-026306-mkmrninv 32 28 ] ] -RRB- cord-026306-mkmrninv 32 29 . . . cord-026306-mkmrninv 33 1 Another another DT cord-026306-mkmrninv 33 2 class class NN cord-026306-mkmrninv 33 3 of of IN cord-026306-mkmrninv 33 4 measures measure NNS cord-026306-mkmrninv 33 5 , , , cord-026306-mkmrninv 33 6 that that WDT cord-026306-mkmrninv 33 7 detect detect VBP cord-026306-mkmrninv 33 8 the the DT cord-026306-mkmrninv 33 9 most most RBS cord-026306-mkmrninv 33 10 important important JJ cord-026306-mkmrninv 33 11 elements element NNS cord-026306-mkmrninv 33 12 , , , cord-026306-mkmrninv 33 13 employs employ VBZ cord-026306-mkmrninv 33 14 cooperative cooperative JJ cord-026306-mkmrninv 33 15 game game NN cord-026306-mkmrninv 33 16 theoretical theoretical JJ cord-026306-mkmrninv 33 17 approach approach NN cord-026306-mkmrninv 33 18 . . . cord-026306-mkmrninv 34 1 It -PRON- PRP cord-026306-mkmrninv 34 2 includes include VBZ cord-026306-mkmrninv 34 3 the the DT cord-026306-mkmrninv 34 4 estimation estimation NN cord-026306-mkmrninv 34 5 of of IN cord-026306-mkmrninv 34 6 Myerson Myerson NNP cord-026306-mkmrninv 34 7 values value NNS cord-026306-mkmrninv 34 8 , , , cord-026306-mkmrninv 34 9 that that RB cord-026306-mkmrninv 34 10 is be VBZ cord-026306-mkmrninv 34 11 similar similar JJ cord-026306-mkmrninv 34 12 to to IN cord-026306-mkmrninv 34 13 Shapley Shapley NNP cord-026306-mkmrninv 34 14 - - HYPH cord-026306-mkmrninv 34 15 Shubik Shubik NNP cord-026306-mkmrninv 34 16 index index NN cord-026306-mkmrninv 34 17 calculation calculation NN cord-026306-mkmrninv 34 18 [ [ -LRB- cord-026306-mkmrninv 34 19 15 15 CD cord-026306-mkmrninv 34 20 ] ] -RRB- cord-026306-mkmrninv 34 21 . . . cord-026306-mkmrninv 35 1 It -PRON- PRP cord-026306-mkmrninv 35 2 also also RB cord-026306-mkmrninv 35 3 requires require VBZ cord-026306-mkmrninv 35 4 the the DT cord-026306-mkmrninv 35 5 introduction introduction NN cord-026306-mkmrninv 35 6 of of IN cord-026306-mkmrninv 35 7 nodes node NNS cord-026306-mkmrninv 35 8 set set VBN cord-026306-mkmrninv 35 9 functions function NNS cord-026306-mkmrninv 35 10 , , , cord-026306-mkmrninv 35 11 that that WDT cord-026306-mkmrninv 35 12 can can MD cord-026306-mkmrninv 35 13 vary vary VB cord-026306-mkmrninv 35 14 depending depend VBG cord-026306-mkmrninv 35 15 on on IN cord-026306-mkmrninv 35 16 the the DT cord-026306-mkmrninv 35 17 problem problem NN cord-026306-mkmrninv 35 18 statement statement NN cord-026306-mkmrninv 35 19 . . . cord-026306-mkmrninv 36 1 In in IN cord-026306-mkmrninv 36 2 [ [ -LRB- cord-026306-mkmrninv 36 3 16 16 CD cord-026306-mkmrninv 36 4 ] ] -RRB- cord-026306-mkmrninv 36 5 the the DT cord-026306-mkmrninv 36 6 Hoede Hoede NNP cord-026306-mkmrninv 36 7 - - HYPH cord-026306-mkmrninv 36 8 Bakker Bakker NNP cord-026306-mkmrninv 36 9 index index NN cord-026306-mkmrninv 36 10 is be VBZ cord-026306-mkmrninv 36 11 adjusted adjust VBN cord-026306-mkmrninv 36 12 to to IN cord-026306-mkmrninv 36 13 the the DT cord-026306-mkmrninv 36 14 estimation estimation NN cord-026306-mkmrninv 36 15 of of IN cord-026306-mkmrninv 36 16 the the DT cord-026306-mkmrninv 36 17 influence influence NN cord-026306-mkmrninv 36 18 elements element NNS cord-026306-mkmrninv 36 19 in in IN cord-026306-mkmrninv 36 20 social social JJ cord-026306-mkmrninv 36 21 networks network NNS cord-026306-mkmrninv 36 22 . . . cord-026306-mkmrninv 37 1 In in IN cord-026306-mkmrninv 37 2 [ [ -LRB- cord-026306-mkmrninv 37 3 17 17 CD cord-026306-mkmrninv 37 4 ] ] -RRB- cord-026306-mkmrninv 37 5 Long long JJ cord-026306-mkmrninv 37 6 - - HYPH cord-026306-mkmrninv 37 7 Range range NN cord-026306-mkmrninv 37 8 Interaction Interaction NNP cord-026306-mkmrninv 37 9 Centrality centrality NN cord-026306-mkmrninv 37 10 ( ( -LRB- cord-026306-mkmrninv 37 11 LRIC LRIC NNP cord-026306-mkmrninv 37 12 ) ) -RRB- cord-026306-mkmrninv 37 13 is be VBZ cord-026306-mkmrninv 37 14 proposed propose VBN cord-026306-mkmrninv 37 15 , , , cord-026306-mkmrninv 37 16 that that WDT cord-026306-mkmrninv 37 17 estimates estimate VBZ cord-026306-mkmrninv 37 18 node node NN cord-026306-mkmrninv 37 19 - - HYPH cord-026306-mkmrninv 37 20 to to IN cord-026306-mkmrninv 37 21 - - HYPH cord-026306-mkmrninv 37 22 node node NN cord-026306-mkmrninv 37 23 influence influence NN cord-026306-mkmrninv 37 24 with with IN cord-026306-mkmrninv 37 25 respect respect NN cord-026306-mkmrninv 37 26 to to IN cord-026306-mkmrninv 37 27 individual individual JJ cord-026306-mkmrninv 37 28 attributes attribute NNS cord-026306-mkmrninv 37 29 of of IN cord-026306-mkmrninv 37 30 nodes node NNS cord-026306-mkmrninv 37 31 , , , cord-026306-mkmrninv 37 32 the the DT cord-026306-mkmrninv 37 33 possibility possibility NN cord-026306-mkmrninv 37 34 of of IN cord-026306-mkmrninv 37 35 the the DT cord-026306-mkmrninv 37 36 group group NN cord-026306-mkmrninv 37 37 influence influence NN cord-026306-mkmrninv 37 38 and and CC cord-026306-mkmrninv 37 39 indirect indirect JJ cord-026306-mkmrninv 37 40 interactions interaction NNS cord-026306-mkmrninv 37 41 through through IN cord-026306-mkmrninv 37 42 intermediate intermediate JJ cord-026306-mkmrninv 37 43 nodes node NNS cord-026306-mkmrninv 37 44 . . . cord-026306-mkmrninv 38 1 However however RB cord-026306-mkmrninv 38 2 , , , cord-026306-mkmrninv 38 3 all all PDT cord-026306-mkmrninv 38 4 the the DT cord-026306-mkmrninv 38 5 approaches approach NNS cord-026306-mkmrninv 38 6 described describe VBN cord-026306-mkmrninv 38 7 above above RB cord-026306-mkmrninv 38 8 are be VBP cord-026306-mkmrninv 38 9 designed design VBN cord-026306-mkmrninv 38 10 for for IN cord-026306-mkmrninv 38 11 so so RB cord-026306-mkmrninv 38 12 - - HYPH cord-026306-mkmrninv 38 13 called call VBN cord-026306-mkmrninv 38 14 monoplex monoplex NN cord-026306-mkmrninv 38 15 networks network NNS cord-026306-mkmrninv 38 16 and and CC cord-026306-mkmrninv 38 17 require require VB cord-026306-mkmrninv 38 18 adaptation adaptation NN cord-026306-mkmrninv 38 19 to to IN cord-026306-mkmrninv 38 20 complex complex JJ cord-026306-mkmrninv 38 21 structures structure NNS cord-026306-mkmrninv 38 22 with with IN cord-026306-mkmrninv 38 23 many many JJ cord-026306-mkmrninv 38 24 types type NNS cord-026306-mkmrninv 38 25 of of IN cord-026306-mkmrninv 38 26 interactions interaction NNS cord-026306-mkmrninv 38 27 between between IN cord-026306-mkmrninv 38 28 adjacent adjacent JJ cord-026306-mkmrninv 38 29 nodes node NNS cord-026306-mkmrninv 38 30 ( ( -LRB- cord-026306-mkmrninv 38 31 so so RB cord-026306-mkmrninv 38 32 - - HYPH cord-026306-mkmrninv 38 33 called call VBN cord-026306-mkmrninv 38 34 multilayer multilayer JJ cord-026306-mkmrninv 38 35 networks network NNS cord-026306-mkmrninv 38 36 [ [ -LRB- cord-026306-mkmrninv 38 37 18 18 CD cord-026306-mkmrninv 38 38 ] ] -RRB- cord-026306-mkmrninv 38 39 ) ) -RRB- cord-026306-mkmrninv 38 40 . . . cord-026306-mkmrninv 39 1 In in IN cord-026306-mkmrninv 39 2 recent recent JJ cord-026306-mkmrninv 39 3 years year NNS cord-026306-mkmrninv 39 4 multilayer multilayer NN cord-026306-mkmrninv 39 5 networks network NNS cord-026306-mkmrninv 39 6 became become VBD cord-026306-mkmrninv 39 7 one one CD cord-026306-mkmrninv 39 8 of of IN cord-026306-mkmrninv 39 9 the the DT cord-026306-mkmrninv 39 10 central central JJ cord-026306-mkmrninv 39 11 topics topic NNS cord-026306-mkmrninv 39 12 in in IN cord-026306-mkmrninv 39 13 the the DT cord-026306-mkmrninv 39 14 field field NN cord-026306-mkmrninv 39 15 of of IN cord-026306-mkmrninv 39 16 network network NN cord-026306-mkmrninv 39 17 science science NN cord-026306-mkmrninv 39 18 . . . cord-026306-mkmrninv 40 1 A a DT cord-026306-mkmrninv 40 2 multilayer multilayer JJ cord-026306-mkmrninv 40 3 network network NN cord-026306-mkmrninv 40 4 where where WRB cord-026306-mkmrninv 40 5 the the DT cord-026306-mkmrninv 40 6 set set NN cord-026306-mkmrninv 40 7 of of IN cord-026306-mkmrninv 40 8 nodes node NNS cord-026306-mkmrninv 40 9 ( ( -LRB- cord-026306-mkmrninv 40 10 or or CC cord-026306-mkmrninv 40 11 a a DT cord-026306-mkmrninv 40 12 part part NN cord-026306-mkmrninv 40 13 of of IN cord-026306-mkmrninv 40 14 nodes node NNS cord-026306-mkmrninv 40 15 ) ) -RRB- cord-026306-mkmrninv 40 16 remains remain VBZ cord-026306-mkmrninv 40 17 the the DT cord-026306-mkmrninv 40 18 same same JJ cord-026306-mkmrninv 40 19 through through IN cord-026306-mkmrninv 40 20 all all DT cord-026306-mkmrninv 40 21 layers layer NNS cord-026306-mkmrninv 40 22 is be VBZ cord-026306-mkmrninv 40 23 called call VBN cord-026306-mkmrninv 40 24 multiplex multiplex NN cord-026306-mkmrninv 40 25 network network NN cord-026306-mkmrninv 40 26 , , , cord-026306-mkmrninv 40 27 which which WDT cord-026306-mkmrninv 40 28 is be VBZ cord-026306-mkmrninv 40 29 the the DT cord-026306-mkmrninv 40 30 object object NN cord-026306-mkmrninv 40 31 of of IN cord-026306-mkmrninv 40 32 the the DT cord-026306-mkmrninv 40 33 research research NN cord-026306-mkmrninv 40 34 in in IN cord-026306-mkmrninv 40 35 this this DT cord-026306-mkmrninv 40 36 work work NN cord-026306-mkmrninv 40 37 . . . cord-026306-mkmrninv 41 1 There there EX cord-026306-mkmrninv 41 2 exist exist VBP cord-026306-mkmrninv 41 3 several several JJ cord-026306-mkmrninv 41 4 ways way NNS cord-026306-mkmrninv 41 5 for for IN cord-026306-mkmrninv 41 6 the the DT cord-026306-mkmrninv 41 7 assessment assessment NN cord-026306-mkmrninv 41 8 of of IN cord-026306-mkmrninv 41 9 central central JJ cord-026306-mkmrninv 41 10 elements element NNS cord-026306-mkmrninv 41 11 in in IN cord-026306-mkmrninv 41 12 multiplex multiplex NN cord-026306-mkmrninv 41 13 networks network NNS cord-026306-mkmrninv 41 14 . . . cord-026306-mkmrninv 42 1 Firstly firstly RB cord-026306-mkmrninv 42 2 , , , cord-026306-mkmrninv 42 3 one one PRP cord-026306-mkmrninv 42 4 can can MD cord-026306-mkmrninv 42 5 calculate calculate VB cord-026306-mkmrninv 42 6 centralities centrality NNS cord-026306-mkmrninv 42 7 for for IN cord-026306-mkmrninv 42 8 each each DT cord-026306-mkmrninv 42 9 layer layer NN cord-026306-mkmrninv 42 10 separately separately RB cord-026306-mkmrninv 42 11 and and CC cord-026306-mkmrninv 42 12 further further JJ cord-026306-mkmrninv 42 13 aggregate aggregate VBP cord-026306-mkmrninv 42 14 the the DT cord-026306-mkmrninv 42 15 obtained obtain VBN cord-026306-mkmrninv 42 16 values value NNS cord-026306-mkmrninv 42 17 through through IN cord-026306-mkmrninv 42 18 all all DT cord-026306-mkmrninv 42 19 considered consider VBN cord-026306-mkmrninv 42 20 networks network NNS cord-026306-mkmrninv 42 21 . . . cord-026306-mkmrninv 43 1 Secondly secondly RB cord-026306-mkmrninv 43 2 , , , cord-026306-mkmrninv 43 3 one one PRP cord-026306-mkmrninv 43 4 can can MD cord-026306-mkmrninv 43 5 aggregate aggregate VB cord-026306-mkmrninv 43 6 connections connection NNS cord-026306-mkmrninv 43 7 between between IN cord-026306-mkmrninv 43 8 pairs pair NNS cord-026306-mkmrninv 43 9 of of IN cord-026306-mkmrninv 43 10 nodes node NNS cord-026306-mkmrninv 43 11 to to TO cord-026306-mkmrninv 43 12 obtain obtain VB cord-026306-mkmrninv 43 13 monoplex monoplex NNP cord-026306-mkmrninv 43 14 network network NN cord-026306-mkmrninv 43 15 and and CC cord-026306-mkmrninv 43 16 then then RB cord-026306-mkmrninv 43 17 apply apply VB cord-026306-mkmrninv 43 18 centrality centrality NN cord-026306-mkmrninv 43 19 measures measure NNS cord-026306-mkmrninv 43 20 to to IN cord-026306-mkmrninv 43 21 a a DT cord-026306-mkmrninv 43 22 new new JJ cord-026306-mkmrninv 43 23 weighted weighted JJ cord-026306-mkmrninv 43 24 graph graph NN cord-026306-mkmrninv 43 25 . . . cord-026306-mkmrninv 44 1 The the DT cord-026306-mkmrninv 44 2 mod mod NN cord-026306-mkmrninv 44 3 - - HYPH cord-026306-mkmrninv 44 4 ification ification NN cord-026306-mkmrninv 44 5 of of IN cord-026306-mkmrninv 44 6 classical classical JJ cord-026306-mkmrninv 44 7 centrality centrality NN cord-026306-mkmrninv 44 8 measures measure NNS cord-026306-mkmrninv 44 9 to to IN cord-026306-mkmrninv 44 10 interconnected interconnect VBN cord-026306-mkmrninv 44 11 multilayer multilayer JJ cord-026306-mkmrninv 44 12 networks network NNS cord-026306-mkmrninv 44 13 is be VBZ cord-026306-mkmrninv 44 14 described describe VBN cord-026306-mkmrninv 44 15 in in IN cord-026306-mkmrninv 44 16 [ [ -LRB- cord-026306-mkmrninv 44 17 18 18 CD cord-026306-mkmrninv 44 18 , , , cord-026306-mkmrninv 44 19 19 19 CD cord-026306-mkmrninv 44 20 ] ] -RRB- cord-026306-mkmrninv 44 21 . . . cord-026306-mkmrninv 45 1 In in IN cord-026306-mkmrninv 45 2 [ [ -LRB- cord-026306-mkmrninv 45 3 20 20 CD cord-026306-mkmrninv 45 4 ] ] -RRB- cord-026306-mkmrninv 45 5 social social JJ cord-026306-mkmrninv 45 6 choice choice NN cord-026306-mkmrninv 45 7 theory theory NN cord-026306-mkmrninv 45 8 rules rule NNS cord-026306-mkmrninv 45 9 are be VBP cord-026306-mkmrninv 45 10 applied apply VBN cord-026306-mkmrninv 45 11 to to IN cord-026306-mkmrninv 45 12 multiplex multiplex JJ cord-026306-mkmrninv 45 13 networks network NNS cord-026306-mkmrninv 45 14 in in IN cord-026306-mkmrninv 45 15 order order NN cord-026306-mkmrninv 45 16 to to TO cord-026306-mkmrninv 45 17 detect detect VB cord-026306-mkmrninv 45 18 key key JJ cord-026306-mkmrninv 45 19 elements element NNS cord-026306-mkmrninv 45 20 . . . cord-026306-mkmrninv 46 1 However however RB cord-026306-mkmrninv 46 2 , , , cord-026306-mkmrninv 46 3 the the DT cord-026306-mkmrninv 46 4 final final JJ cord-026306-mkmrninv 46 5 results result NNS cord-026306-mkmrninv 46 6 for for IN cord-026306-mkmrninv 46 7 these these DT cord-026306-mkmrninv 46 8 approaches approach NNS cord-026306-mkmrninv 46 9 are be VBP cord-026306-mkmrninv 46 10 calculated calculate VBN cord-026306-mkmrninv 46 11 from from IN cord-026306-mkmrninv 46 12 the the DT cord-026306-mkmrninv 46 13 secondary secondary JJ cord-026306-mkmrninv 46 14 data datum NNS cord-026306-mkmrninv 46 15 . . . cord-026306-mkmrninv 47 1 In in IN cord-026306-mkmrninv 47 2 this this DT cord-026306-mkmrninv 47 3 work work NN cord-026306-mkmrninv 47 4 we -PRON- PRP cord-026306-mkmrninv 47 5 propose propose VBP cord-026306-mkmrninv 47 6 a a DT cord-026306-mkmrninv 47 7 novel novel JJ cord-026306-mkmrninv 47 8 technique technique NN cord-026306-mkmrninv 47 9 of of IN cord-026306-mkmrninv 47 10 the the DT cord-026306-mkmrninv 47 11 key key JJ cord-026306-mkmrninv 47 12 elements element NNS cord-026306-mkmrninv 47 13 assessment assessment NN cord-026306-mkmrninv 47 14 . . . cord-026306-mkmrninv 48 1 We -PRON- PRP cord-026306-mkmrninv 48 2 construct construct VBP cord-026306-mkmrninv 48 3 a a DT cord-026306-mkmrninv 48 4 mapping mapping NN cord-026306-mkmrninv 48 5 between between IN cord-026306-mkmrninv 48 6 each each DT cord-026306-mkmrninv 48 7 node node NN cord-026306-mkmrninv 48 8 and and CC cord-026306-mkmrninv 48 9 sets set NNS cord-026306-mkmrninv 48 10 of of IN cord-026306-mkmrninv 48 11 other other JJ cord-026306-mkmrninv 48 12 nodes node NNS cord-026306-mkmrninv 48 13 , , , cord-026306-mkmrninv 48 14 which which WDT cord-026306-mkmrninv 48 15 is be VBZ cord-026306-mkmrninv 48 16 a a DT cord-026306-mkmrninv 48 17 mass mass JJ cord-026306-mkmrninv 48 18 function function NN cord-026306-mkmrninv 48 19 . . . cord-026306-mkmrninv 49 1 In in IN cord-026306-mkmrninv 49 2 case case NN cord-026306-mkmrninv 49 3 of of IN cord-026306-mkmrninv 49 4 several several JJ cord-026306-mkmrninv 49 5 layers layer NNS cord-026306-mkmrninv 49 6 we -PRON- PRP cord-026306-mkmrninv 49 7 combine combine VBP cord-026306-mkmrninv 49 8 mass mass JJ cord-026306-mkmrninv 49 9 functions function NNS cord-026306-mkmrninv 49 10 on on IN cord-026306-mkmrninv 49 11 each each DT cord-026306-mkmrninv 49 12 layer layer NN cord-026306-mkmrninv 49 13 to to IN cord-026306-mkmrninv 49 14 a a DT cord-026306-mkmrninv 49 15 unique unique JJ cord-026306-mkmrninv 49 16 function function NN cord-026306-mkmrninv 49 17 that that WDT cord-026306-mkmrninv 49 18 can can MD cord-026306-mkmrninv 49 19 be be VB cord-026306-mkmrninv 49 20 used use VBN cord-026306-mkmrninv 49 21 for for IN cord-026306-mkmrninv 49 22 the the DT cord-026306-mkmrninv 49 23 centrality centrality NN cord-026306-mkmrninv 49 24 estimation estimation NN cord-026306-mkmrninv 49 25 in in IN cord-026306-mkmrninv 49 26 the the DT cord-026306-mkmrninv 49 27 whole whole JJ cord-026306-mkmrninv 49 28 system system NN cord-026306-mkmrninv 49 29 . . . cord-026306-mkmrninv 50 1 The the DT cord-026306-mkmrninv 50 2 key key JJ cord-026306-mkmrninv 50 3 advantages advantage NNS cord-026306-mkmrninv 50 4 of of IN cord-026306-mkmrninv 50 5 our -PRON- PRP$ cord-026306-mkmrninv 50 6 approach approach NN cord-026306-mkmrninv 50 7 are be VBP cord-026306-mkmrninv 50 8 that that IN cord-026306-mkmrninv 50 9 we -PRON- PRP cord-026306-mkmrninv 50 10 take take VBP cord-026306-mkmrninv 50 11 into into IN cord-026306-mkmrninv 50 12 account account NN cord-026306-mkmrninv 50 13 interactions interaction NNS cord-026306-mkmrninv 50 14 with with IN cord-026306-mkmrninv 50 15 different different JJ cord-026306-mkmrninv 50 16 groups group NNS cord-026306-mkmrninv 50 17 of of IN cord-026306-mkmrninv 50 18 nodes node NNS cord-026306-mkmrninv 50 19 and and CC cord-026306-mkmrninv 50 20 we -PRON- PRP cord-026306-mkmrninv 50 21 are be VBP cord-026306-mkmrninv 50 22 able able JJ cord-026306-mkmrninv 50 23 to to TO cord-026306-mkmrninv 50 24 estimate estimate VB cord-026306-mkmrninv 50 25 node node NN cord-026306-mkmrninv 50 26 - - HYPH cord-026306-mkmrninv 50 27 to to IN cord-026306-mkmrninv 50 28 - - HYPH cord-026306-mkmrninv 50 29 node node NN cord-026306-mkmrninv 50 30 influence influence NN cord-026306-mkmrninv 50 31 within within IN cord-026306-mkmrninv 50 32 the the DT cord-026306-mkmrninv 50 33 whole whole JJ cord-026306-mkmrninv 50 34 network network NN cord-026306-mkmrninv 50 35 structure structure NN cord-026306-mkmrninv 50 36 . . . cord-026306-mkmrninv 51 1 We -PRON- PRP cord-026306-mkmrninv 51 2 also also RB cord-026306-mkmrninv 51 3 take take VBP cord-026306-mkmrninv 51 4 into into IN cord-026306-mkmrninv 51 5 account account NN cord-026306-mkmrninv 51 6 the the DT cord-026306-mkmrninv 51 7 consistency consistency NN cord-026306-mkmrninv 51 8 on on IN cord-026306-mkmrninv 51 9 connections connection NNS cord-026306-mkmrninv 51 10 on on IN cord-026306-mkmrninv 51 11 different different JJ cord-026306-mkmrninv 51 12 network network NN cord-026306-mkmrninv 51 13 layers layer NNS cord-026306-mkmrninv 51 14 . . . cord-026306-mkmrninv 52 1 This this DT cord-026306-mkmrninv 52 2 paper paper NN cord-026306-mkmrninv 52 3 is be VBZ cord-026306-mkmrninv 52 4 organized organize VBN cord-026306-mkmrninv 52 5 as as IN cord-026306-mkmrninv 52 6 follows follow VBZ cord-026306-mkmrninv 52 7 : : : cord-026306-mkmrninv 52 8 in in IN cord-026306-mkmrninv 52 9 Sect Sect NNP cord-026306-mkmrninv 52 10 . . . cord-026306-mkmrninv 53 1 2 2 LS cord-026306-mkmrninv 53 2 we -PRON- PRP cord-026306-mkmrninv 53 3 describe describe VBP cord-026306-mkmrninv 53 4 some some DT cord-026306-mkmrninv 53 5 basic basic JJ cord-026306-mkmrninv 53 6 concepts concept NNS cord-026306-mkmrninv 53 7 from from IN cord-026306-mkmrninv 53 8 belief belief NN cord-026306-mkmrninv 53 9 functions function NNS cord-026306-mkmrninv 53 10 theory theory NN cord-026306-mkmrninv 53 11 . . . cord-026306-mkmrninv 54 1 In in IN cord-026306-mkmrninv 54 2 Sect Sect NNP cord-026306-mkmrninv 54 3 . . . cord-026306-mkmrninv 55 1 3 3 LS cord-026306-mkmrninv 55 2 we -PRON- PRP cord-026306-mkmrninv 55 3 propose propose VBP cord-026306-mkmrninv 55 4 a a DT cord-026306-mkmrninv 55 5 centrality centrality NN cord-026306-mkmrninv 55 6 measure measure NN cord-026306-mkmrninv 55 7 for for IN cord-026306-mkmrninv 55 8 onelayer onelayer NNP cord-026306-mkmrninv 55 9 network network NN cord-026306-mkmrninv 55 10 and and CC cord-026306-mkmrninv 55 11 apply apply VB cord-026306-mkmrninv 55 12 it -PRON- PRP cord-026306-mkmrninv 55 13 to to IN cord-026306-mkmrninv 55 14 a a DT cord-026306-mkmrninv 55 15 toy toy NN cord-026306-mkmrninv 55 16 example example NN cord-026306-mkmrninv 55 17 . . . cord-026306-mkmrninv 56 1 In in IN cord-026306-mkmrninv 56 2 Sect Sect NNP cord-026306-mkmrninv 56 3 . . . cord-026306-mkmrninv 57 1 4 4 LS cord-026306-mkmrninv 57 2 we -PRON- PRP cord-026306-mkmrninv 57 3 develop develop VBP cord-026306-mkmrninv 57 4 an an DT cord-026306-mkmrninv 57 5 approach approach NN cord-026306-mkmrninv 57 6 to to TO cord-026306-mkmrninv 57 7 elucidate elucidate VB cord-026306-mkmrninv 57 8 important important JJ cord-026306-mkmrninv 57 9 elements element NNS cord-026306-mkmrninv 57 10 in in IN cord-026306-mkmrninv 57 11 networks network NNS cord-026306-mkmrninv 57 12 with with IN cord-026306-mkmrninv 57 13 several several JJ cord-026306-mkmrninv 57 14 layers layer NNS cord-026306-mkmrninv 57 15 . . . cord-026306-mkmrninv 58 1 In in IN cord-026306-mkmrninv 58 2 the the DT cord-026306-mkmrninv 58 3 same same JJ cord-026306-mkmrninv 58 4 Section section NN cord-026306-mkmrninv 58 5 we -PRON- PRP cord-026306-mkmrninv 58 6 apply apply VBP cord-026306-mkmrninv 58 7 the the DT cord-026306-mkmrninv 58 8 proposed propose VBN cord-026306-mkmrninv 58 9 method method NN cord-026306-mkmrninv 58 10 to to IN cord-026306-mkmrninv 58 11 two two CD cord-026306-mkmrninv 58 12 - - HYPH cord-026306-mkmrninv 58 13 layers layer NNS cord-026306-mkmrninv 58 14 network network NN cord-026306-mkmrninv 58 15 . . . cord-026306-mkmrninv 59 1 Section section NN cord-026306-mkmrninv 59 2 5 5 CD cord-026306-mkmrninv 59 3 contains contain VBZ cord-026306-mkmrninv 59 4 a a DT cord-026306-mkmrninv 59 5 discussion discussion NN cord-026306-mkmrninv 59 6 of of IN cord-026306-mkmrninv 59 7 our -PRON- PRP$ cord-026306-mkmrninv 59 8 approach approach NN cord-026306-mkmrninv 59 9 as as RB cord-026306-mkmrninv 59 10 well well RB cord-026306-mkmrninv 59 11 as as IN cord-026306-mkmrninv 59 12 conclusion conclusion NN cord-026306-mkmrninv 59 13 to to IN cord-026306-mkmrninv 59 14 the the DT cord-026306-mkmrninv 59 15 work work NN cord-026306-mkmrninv 59 16 . . . cord-026306-mkmrninv 60 1 In in IN cord-026306-mkmrninv 60 2 this this DT cord-026306-mkmrninv 60 3 Section section NN cord-026306-mkmrninv 60 4 we -PRON- PRP cord-026306-mkmrninv 60 5 will will MD cord-026306-mkmrninv 60 6 remind remind VB cord-026306-mkmrninv 60 7 some some DT cord-026306-mkmrninv 60 8 basic basic JJ cord-026306-mkmrninv 60 9 definitions definition NNS cord-026306-mkmrninv 60 10 and and CC cord-026306-mkmrninv 60 11 notions notion NNS cord-026306-mkmrninv 60 12 from from IN cord-026306-mkmrninv 60 13 Dempster Dempster NNP cord-026306-mkmrninv 60 14 - - HYPH cord-026306-mkmrninv 60 15 Shafer Shafer NNP cord-026306-mkmrninv 60 16 theory theory NN cord-026306-mkmrninv 60 17 of of IN cord-026306-mkmrninv 60 18 belief belief NN cord-026306-mkmrninv 60 19 functions function NNS cord-026306-mkmrninv 60 20 [ [ -LRB- cord-026306-mkmrninv 60 21 1 1 CD cord-026306-mkmrninv 60 22 , , , cord-026306-mkmrninv 60 23 2 2 CD cord-026306-mkmrninv 60 24 ] ] -RRB- cord-026306-mkmrninv 60 25 that that WDT cord-026306-mkmrninv 60 26 are be VBP cord-026306-mkmrninv 60 27 further further RB cord-026306-mkmrninv 60 28 employed employ VBN cord-026306-mkmrninv 60 29 in in IN cord-026306-mkmrninv 60 30 this this DT cord-026306-mkmrninv 60 31 work work NN cord-026306-mkmrninv 60 32 . . . cord-026306-mkmrninv 61 1 Let let VB cord-026306-mkmrninv 61 2 X x NN cord-026306-mkmrninv 61 3 be be VB cord-026306-mkmrninv 61 4 a a DT cord-026306-mkmrninv 61 5 finite finite JJ cord-026306-mkmrninv 61 6 set set NN cord-026306-mkmrninv 61 7 that that WDT cord-026306-mkmrninv 61 8 is be VBZ cord-026306-mkmrninv 61 9 called call VBN cord-026306-mkmrninv 61 10 frame frame NN cord-026306-mkmrninv 61 11 of of IN cord-026306-mkmrninv 61 12 discernment discernment NN cord-026306-mkmrninv 61 13 and and CC cord-026306-mkmrninv 61 14 2 2 CD cord-026306-mkmrninv 61 15 X x NN cord-026306-mkmrninv 61 16 is be VBZ cord-026306-mkmrninv 61 17 a a DT cord-026306-mkmrninv 61 18 set set NN cord-026306-mkmrninv 61 19 of of IN cord-026306-mkmrninv 61 20 all all DT cord-026306-mkmrninv 61 21 subsets subset NNS cord-026306-mkmrninv 61 22 of of IN cord-026306-mkmrninv 61 23 X. X. NNP cord-026306-mkmrninv 61 24 Function function NN cord-026306-mkmrninv 61 25 m m NNP cord-026306-mkmrninv 61 26 : : : cord-026306-mkmrninv 62 1 2 2 LS cord-026306-mkmrninv 62 2 X x NN cord-026306-mkmrninv 62 3 → → XX cord-026306-mkmrninv 62 4 [ [ -LRB- cord-026306-mkmrninv 62 5 0 0 NN cord-026306-mkmrninv 62 6 ; ; : cord-026306-mkmrninv 62 7 1 1 LS cord-026306-mkmrninv 62 8 ] ] -RRB- cord-026306-mkmrninv 62 9 that that WDT cord-026306-mkmrninv 62 10 meets meet VBZ cord-026306-mkmrninv 62 11 the the DT cord-026306-mkmrninv 62 12 requirements requirement NNS cord-026306-mkmrninv 62 13 of of IN cord-026306-mkmrninv 62 14 normalization normalization NN cord-026306-mkmrninv 62 15 condition condition NN cord-026306-mkmrninv 62 16 , , , cord-026306-mkmrninv 62 17 i.e. i.e. FW cord-026306-mkmrninv 62 18 m(∅ m(∅ NNP cord-026306-mkmrninv 62 19 ) ) -RRB- cord-026306-mkmrninv 62 20 = = SYM cord-026306-mkmrninv 62 21 0 0 NFP cord-026306-mkmrninv 63 1 and and CC cord-026306-mkmrninv 63 2 A∈2 A∈2 NNP cord-026306-mkmrninv 63 3 X X NNP cord-026306-mkmrninv 63 4 m(A m(A NNP cord-026306-mkmrninv 63 5 ) ) -RRB- cord-026306-mkmrninv 63 6 = = SYM cord-026306-mkmrninv 63 7 1 1 CD cord-026306-mkmrninv 63 8 , , , cord-026306-mkmrninv 63 9 is be VBZ cord-026306-mkmrninv 63 10 called call VBN cord-026306-mkmrninv 63 11 basic basic JJ cord-026306-mkmrninv 63 12 probability probability NN cord-026306-mkmrninv 63 13 assignment assignment NN cord-026306-mkmrninv 63 14 or or CC cord-026306-mkmrninv 63 15 a a DT cord-026306-mkmrninv 63 16 mass mass NN cord-026306-mkmrninv 63 17 function function NN cord-026306-mkmrninv 63 18 . . . cord-026306-mkmrninv 64 1 All all DT cord-026306-mkmrninv 64 2 A a DT cord-026306-mkmrninv 64 3 ∈ ∈ NN cord-026306-mkmrninv 64 4 2 2 CD cord-026306-mkmrninv 64 5 X x NN cord-026306-mkmrninv 64 6 such such JJ cord-026306-mkmrninv 64 7 that that IN cord-026306-mkmrninv 64 8 m(A m(a CD cord-026306-mkmrninv 64 9 ) ) -RRB- cord-026306-mkmrninv 64 10 > > XX cord-026306-mkmrninv 65 1 0 0 NFP cord-026306-mkmrninv 65 2 are be VBP cord-026306-mkmrninv 65 3 called call VBN cord-026306-mkmrninv 65 4 focal focal JJ cord-026306-mkmrninv 65 5 elements element NNS cord-026306-mkmrninv 65 6 and and CC cord-026306-mkmrninv 65 7 the the DT cord-026306-mkmrninv 65 8 family family NN cord-026306-mkmrninv 65 9 of of IN cord-026306-mkmrninv 65 10 all all DT cord-026306-mkmrninv 65 11 focal focal JJ cord-026306-mkmrninv 65 12 elements element NNS cord-026306-mkmrninv 65 13 is be VBZ cord-026306-mkmrninv 65 14 called call VBN cord-026306-mkmrninv 65 15 the the DT cord-026306-mkmrninv 65 16 body body NN cord-026306-mkmrninv 65 17 of of IN cord-026306-mkmrninv 65 18 evidence evidence NN cord-026306-mkmrninv 65 19 . . . cord-026306-mkmrninv 66 1 Mass mass JJ cord-026306-mkmrninv 66 2 function function NN cord-026306-mkmrninv 66 3 m m NN cord-026306-mkmrninv 66 4 can can MD cord-026306-mkmrninv 66 5 be be VB cord-026306-mkmrninv 66 6 associated associate VBN cord-026306-mkmrninv 66 7 with with IN cord-026306-mkmrninv 66 8 two two CD cord-026306-mkmrninv 66 9 set set NN cord-026306-mkmrninv 66 10 functions function NNS cord-026306-mkmrninv 66 11 namely namely RB cord-026306-mkmrninv 66 12 a a DT cord-026306-mkmrninv 66 13 belief belief NN cord-026306-mkmrninv 66 14 function function NN cord-026306-mkmrninv 66 15 denoted denote VBN cord-026306-mkmrninv 66 16 by by IN cord-026306-mkmrninv 66 17 g(A g(A NNP cord-026306-mkmrninv 66 18 ) ) -RRB- cord-026306-mkmrninv 66 19 = = NFP cord-026306-mkmrninv 67 1 B⊂A B⊂A NNP cord-026306-mkmrninv 67 2 m(B m(B NNP cord-026306-mkmrninv 67 3 ) ) -RRB- cord-026306-mkmrninv 67 4 and and CC cord-026306-mkmrninv 67 5 a a DT cord-026306-mkmrninv 67 6 plausibility plausibility NN cord-026306-mkmrninv 67 7 function function NN cord-026306-mkmrninv 67 8 denoted denote VBN cord-026306-mkmrninv 67 9 g(A g(a NN cord-026306-mkmrninv 67 10 ) ) -RRB- cord-026306-mkmrninv 68 1 = = NFP cord-026306-mkmrninv 69 1 B b NN cord-026306-mkmrninv 69 2 : : : cord-026306-mkmrninv 70 1 A∩B A∩B NNP cord-026306-mkmrninv 70 2 = = NNP cord-026306-mkmrninv 70 3 ∅ ∅ NNP cord-026306-mkmrninv 70 4 m(B m(B NNP cord-026306-mkmrninv 70 5 ) ) -RRB- cord-026306-mkmrninv 70 6 , , . cord-026306-mkmrninv 71 1 that that DT cord-026306-mkmrninv 71 2 is be VBZ cord-026306-mkmrninv 71 3 dual dual JJ cord-026306-mkmrninv 71 4 to to IN cord-026306-mkmrninv 71 5 belief belief NN cord-026306-mkmrninv 71 6 function function NN cord-026306-mkmrninv 71 7 g(A g(A NNP cord-026306-mkmrninv 71 8 ) ) -RRB- cord-026306-mkmrninv 71 9 . . . cord-026306-mkmrninv 72 1 These these DT cord-026306-mkmrninv 72 2 two two CD cord-026306-mkmrninv 72 3 functions function NNS cord-026306-mkmrninv 72 4 can can MD cord-026306-mkmrninv 72 5 be be VB cord-026306-mkmrninv 72 6 considered consider VBN cord-026306-mkmrninv 72 7 as as IN cord-026306-mkmrninv 72 8 lower low JJR cord-026306-mkmrninv 72 9 and and CC cord-026306-mkmrninv 72 10 upper upper JJ cord-026306-mkmrninv 72 11 bounds bound NNS cord-026306-mkmrninv 72 12 for for IN cord-026306-mkmrninv 72 13 the the DT cord-026306-mkmrninv 72 14 probability probability NN cord-026306-mkmrninv 72 15 estimation estimation NN cord-026306-mkmrninv 72 16 of of IN cord-026306-mkmrninv 72 17 event event NN cord-026306-mkmrninv 72 18 A a NN cord-026306-mkmrninv 72 19 : : : cord-026306-mkmrninv 72 20 g(A g(a LS cord-026306-mkmrninv 72 21 ) ) -RRB- cord-026306-mkmrninv 72 22 ≤ ≤ NN cord-026306-mkmrninv 72 23 P p NN cord-026306-mkmrninv 72 24 ( ( -LRB- cord-026306-mkmrninv 72 25 A a NN cord-026306-mkmrninv 72 26 ) ) -RRB- cord-026306-mkmrninv 72 27 ≤ḡ(A ≤ḡ(A NNP cord-026306-mkmrninv 72 28 ) ) -RRB- cord-026306-mkmrninv 72 29 , , , cord-026306-mkmrninv 72 30 A a DT cord-026306-mkmrninv 72 31 ∈ ∈ NN cord-026306-mkmrninv 72 32 2 2 CD cord-026306-mkmrninv 72 33 X x NN cord-026306-mkmrninv 72 34 . . . cord-026306-mkmrninv 73 1 The the DT cord-026306-mkmrninv 73 2 value value NN cord-026306-mkmrninv 73 3 of of IN cord-026306-mkmrninv 73 4 function function NN cord-026306-mkmrninv 73 5 g(A g(A NNP cord-026306-mkmrninv 73 6 ) ) -RRB- cord-026306-mkmrninv 73 7 reflects reflect VBZ cord-026306-mkmrninv 73 8 the the DT cord-026306-mkmrninv 73 9 belief belief NN cord-026306-mkmrninv 73 10 level level NN cord-026306-mkmrninv 73 11 to to IN cord-026306-mkmrninv 73 12 the the DT cord-026306-mkmrninv 73 13 fact fact NN cord-026306-mkmrninv 73 14 that that IN cord-026306-mkmrninv 73 15 x x NN cord-026306-mkmrninv 73 16 ∈ ∈ NN cord-026306-mkmrninv 74 1 A a DT cord-026306-mkmrninv 74 2 ⊆ ⊆ NN cord-026306-mkmrninv 74 3 X x NN cord-026306-mkmrninv 74 4 , , , cord-026306-mkmrninv 74 5 where where WRB cord-026306-mkmrninv 74 6 x x NN cord-026306-mkmrninv 74 7 from from IN cord-026306-mkmrninv 74 8 X. X. NNP cord-026306-mkmrninv 75 1 We -PRON- PRP cord-026306-mkmrninv 75 2 denote denote VBP cord-026306-mkmrninv 75 3 by by IN cord-026306-mkmrninv 75 4 Bel(X Bel(X NNP cord-026306-mkmrninv 75 5 ) ) -RRB- cord-026306-mkmrninv 75 6 a a DT cord-026306-mkmrninv 75 7 set set NN cord-026306-mkmrninv 75 8 of of IN cord-026306-mkmrninv 75 9 all all DT cord-026306-mkmrninv 75 10 belief belief NN cord-026306-mkmrninv 75 11 functions function NNS cord-026306-mkmrninv 75 12 g g NN cord-026306-mkmrninv 75 13 on on IN cord-026306-mkmrninv 75 14 set set NN cord-026306-mkmrninv 75 15 X. X. NNP cord-026306-mkmrninv 75 16 Belief belief NN cord-026306-mkmrninv 75 17 function function NN cord-026306-mkmrninv 76 1 g g NN cord-026306-mkmrninv 76 2 can can MD cord-026306-mkmrninv 76 3 be be VB cord-026306-mkmrninv 76 4 also also RB cord-026306-mkmrninv 76 5 represented represent VBN cord-026306-mkmrninv 76 6 as as IN cord-026306-mkmrninv 76 7 a a DT cord-026306-mkmrninv 76 8 convex convex JJ cord-026306-mkmrninv 76 9 combination combination NN cord-026306-mkmrninv 76 10 of of IN cord-026306-mkmrninv 76 11 categor- categor- NN cord-026306-mkmrninv 76 12 . . . cord-026306-mkmrninv 77 1 Note note VB cord-026306-mkmrninv 77 2 that that IN cord-026306-mkmrninv 77 3 η η NN cord-026306-mkmrninv 77 4 X x NN cord-026306-mkmrninv 77 5 describes describe VBZ cord-026306-mkmrninv 77 6 vacuous vacuous JJ cord-026306-mkmrninv 77 7 evidence evidence NN cord-026306-mkmrninv 77 8 that that IN cord-026306-mkmrninv 77 9 x x NN cord-026306-mkmrninv 77 10 ∈ ∈ NN cord-026306-mkmrninv 77 11 X. x. NN cord-026306-mkmrninv 78 1 Thus thus RB cord-026306-mkmrninv 78 2 , , , cord-026306-mkmrninv 78 3 we -PRON- PRP cord-026306-mkmrninv 78 4 call call VBP cord-026306-mkmrninv 78 5 this this DT cord-026306-mkmrninv 78 6 function function NN cord-026306-mkmrninv 78 7 as as IN cord-026306-mkmrninv 78 8 vacuous vacuous JJ cord-026306-mkmrninv 78 9 belief belief NN cord-026306-mkmrninv 78 10 function function NN cord-026306-mkmrninv 78 11 . . . cord-026306-mkmrninv 79 1 Additionally additionally RB cord-026306-mkmrninv 79 2 , , , cord-026306-mkmrninv 79 3 mass mass NN cord-026306-mkmrninv 79 4 function function NN cord-026306-mkmrninv 79 5 m(A m(a CD cord-026306-mkmrninv 79 6 ) ) -RRB- cord-026306-mkmrninv 79 7 can can MD cord-026306-mkmrninv 79 8 be be VB cord-026306-mkmrninv 79 9 also also RB cord-026306-mkmrninv 79 10 expressed express VBN cord-026306-mkmrninv 79 11 from from IN cord-026306-mkmrninv 79 12 belief belief NN cord-026306-mkmrninv 79 13 function function NN cord-026306-mkmrninv 79 14 g g NN cord-026306-mkmrninv 79 15 with with IN cord-026306-mkmrninv 79 16 Möbius möbius JJ cord-026306-mkmrninv 79 17 transformation transformation NN cord-026306-mkmrninv 79 18 as as IN cord-026306-mkmrninv 79 19 m(A m(a CD cord-026306-mkmrninv 79 20 ) ) -RRB- cord-026306-mkmrninv 80 1 = = NFP cord-026306-mkmrninv 81 1 B⊂A B⊂A NNP cord-026306-mkmrninv 81 2 ( ( -LRB- cord-026306-mkmrninv 81 3 −1 −1 NNP cord-026306-mkmrninv 81 4 ) ) -RRB- cord-026306-mkmrninv 82 1 |A\B| |A\B| NNP cord-026306-mkmrninv 82 2 g g NN cord-026306-mkmrninv 82 3 ( ( -LRB- cord-026306-mkmrninv 82 4 B b NN cord-026306-mkmrninv 82 5 ) ) -RRB- cord-026306-mkmrninv 82 6 . . . cord-026306-mkmrninv 83 1 In in IN cord-026306-mkmrninv 83 2 this this DT cord-026306-mkmrninv 83 3 work work NN cord-026306-mkmrninv 83 4 we -PRON- PRP cord-026306-mkmrninv 83 5 mainly mainly RB cord-026306-mkmrninv 83 6 focus focus VBP cord-026306-mkmrninv 83 7 on on IN cord-026306-mkmrninv 83 8 combination combination NN cord-026306-mkmrninv 83 9 techniques technique NNS cord-026306-mkmrninv 83 10 adopted adopt VBN cord-026306-mkmrninv 83 11 from from IN cord-026306-mkmrninv 83 12 Dempster Dempster NNP cord-026306-mkmrninv 83 13 - - HYPH cord-026306-mkmrninv 83 14 Shafer Shafer NNP cord-026306-mkmrninv 83 15 theory theory NN cord-026306-mkmrninv 83 16 . . . cord-026306-mkmrninv 84 1 By by IN cord-026306-mkmrninv 84 2 combination combination NN cord-026306-mkmrninv 84 3 we -PRON- PRP cord-026306-mkmrninv 84 4 mean mean VBP cord-026306-mkmrninv 84 5 some some DT cord-026306-mkmrninv 84 6 operator operator NN cord-026306-mkmrninv 84 7 R r NN cord-026306-mkmrninv 84 8 : : : cord-026306-mkmrninv 84 9 Bel(X Bel(X NNP cord-026306-mkmrninv 84 10 ) ) -RRB- cord-026306-mkmrninv 84 11 × × NNP cord-026306-mkmrninv 84 12 Bel(x Bel(x NNP cord-026306-mkmrninv 84 13 ) ) -RRB- cord-026306-mkmrninv 85 1 → → IN cord-026306-mkmrninv 85 2 Bel(X Bel(X NNP cord-026306-mkmrninv 85 3 ) ) -RRB- cord-026306-mkmrninv 85 4 that that WDT cord-026306-mkmrninv 85 5 transforms transform VBZ cord-026306-mkmrninv 85 6 two two CD cord-026306-mkmrninv 85 7 belief belief NN cord-026306-mkmrninv 85 8 functions function NNS cord-026306-mkmrninv 85 9 into into IN cord-026306-mkmrninv 85 10 one one CD cord-026306-mkmrninv 85 11 belief belief NN cord-026306-mkmrninv 85 12 function function NN cord-026306-mkmrninv 85 13 . . . cord-026306-mkmrninv 86 1 We -PRON- PRP cord-026306-mkmrninv 86 2 denote denote VBP cord-026306-mkmrninv 86 3 by by IN cord-026306-mkmrninv 86 4 m m NNP cord-026306-mkmrninv 86 5 = = SYM cord-026306-mkmrninv 86 6 m m NN cord-026306-mkmrninv 86 7 1 1 CD cord-026306-mkmrninv 87 1 ⊗ ⊗ NNP cord-026306-mkmrninv 87 2 R R NNP cord-026306-mkmrninv 87 3 m m NN cord-026306-mkmrninv 87 4 2 2 CD cord-026306-mkmrninv 87 5 the the DT cord-026306-mkmrninv 87 6 combinations combination NNS cord-026306-mkmrninv 87 7 of of IN cord-026306-mkmrninv 87 8 two two CD cord-026306-mkmrninv 87 9 mass mass NN cord-026306-mkmrninv 87 10 functions function NNS cord-026306-mkmrninv 87 11 m m NNP cord-026306-mkmrninv 87 12 1 1 CD cord-026306-mkmrninv 87 13 and and CC cord-026306-mkmrninv 87 14 m m CD cord-026306-mkmrninv 87 15 2 2 CD cord-026306-mkmrninv 87 16 under under IN cord-026306-mkmrninv 87 17 rule rule NN cord-026306-mkmrninv 88 1 R. R. NNP cord-026306-mkmrninv 88 2 There there EX cord-026306-mkmrninv 88 3 exist exist VBP cord-026306-mkmrninv 88 4 various various JJ cord-026306-mkmrninv 88 5 combination combination NN cord-026306-mkmrninv 88 6 rules rule NNS cord-026306-mkmrninv 88 7 that that WDT cord-026306-mkmrninv 88 8 are be VBP cord-026306-mkmrninv 88 9 widely widely RB cord-026306-mkmrninv 88 10 used use VBN cord-026306-mkmrninv 88 11 in in IN cord-026306-mkmrninv 88 12 the the DT cord-026306-mkmrninv 88 13 theory theory NN cord-026306-mkmrninv 88 14 and and CC cord-026306-mkmrninv 88 15 applications application NNS cord-026306-mkmrninv 88 16 of of IN cord-026306-mkmrninv 88 17 belief belief NN cord-026306-mkmrninv 88 18 functions function NNS cord-026306-mkmrninv 88 19 . . . cord-026306-mkmrninv 89 1 For for IN cord-026306-mkmrninv 89 2 instance instance NN cord-026306-mkmrninv 89 3 , , , cord-026306-mkmrninv 89 4 Dempster Dempster NNP cord-026306-mkmrninv 89 5 rule rule NN cord-026306-mkmrninv 89 6 [ [ -LRB- cord-026306-mkmrninv 89 7 1 1 CD cord-026306-mkmrninv 89 8 ] ] -RRB- cord-026306-mkmrninv 89 9 , , , cord-026306-mkmrninv 89 10 that that WDT cord-026306-mkmrninv 89 11 is be VBZ cord-026306-mkmrninv 89 12 regarded regard VBN cord-026306-mkmrninv 89 13 as as IN cord-026306-mkmrninv 89 14 the the DT cord-026306-mkmrninv 89 15 pioneered pioneer VBN cord-026306-mkmrninv 89 16 and and CC cord-026306-mkmrninv 89 17 the the DT cord-026306-mkmrninv 89 18 most most RBS cord-026306-mkmrninv 89 19 popular popular JJ cord-026306-mkmrninv 89 20 combination combination NN cord-026306-mkmrninv 89 21 technique technique NN cord-026306-mkmrninv 89 22 in in IN cord-026306-mkmrninv 89 23 Dempster Dempster NNP cord-026306-mkmrninv 89 24 - - HYPH cord-026306-mkmrninv 89 25 Shafer Shafer NNP cord-026306-mkmrninv 89 26 theory theory NN cord-026306-mkmrninv 89 27 , , , cord-026306-mkmrninv 89 28 is be VBZ cord-026306-mkmrninv 89 29 calculated calculate VBN cord-026306-mkmrninv 89 30 as as IN cord-026306-mkmrninv 89 31 follows follow VBZ cord-026306-mkmrninv 89 32 : : : cord-026306-mkmrninv 89 33 indicates indicate VBZ cord-026306-mkmrninv 89 34 the the DT cord-026306-mkmrninv 89 35 level level NN cord-026306-mkmrninv 89 36 of of IN cord-026306-mkmrninv 89 37 conflict conflict NN cord-026306-mkmrninv 89 38 between between IN cord-026306-mkmrninv 89 39 two two CD cord-026306-mkmrninv 89 40 evidences evidence NNS cord-026306-mkmrninv 89 41 . . . cord-026306-mkmrninv 90 1 If if IN cord-026306-mkmrninv 90 2 K K NNP cord-026306-mkmrninv 90 3 = = SYM cord-026306-mkmrninv 90 4 1 1 CD cord-026306-mkmrninv 90 5 then then RB cord-026306-mkmrninv 90 6 the the DT cord-026306-mkmrninv 90 7 level level NN cord-026306-mkmrninv 90 8 of of IN cord-026306-mkmrninv 90 9 conflict conflict NN cord-026306-mkmrninv 90 10 is be VBZ cord-026306-mkmrninv 90 11 the the DT cord-026306-mkmrninv 90 12 highest high JJS cord-026306-mkmrninv 90 13 and and CC cord-026306-mkmrninv 90 14 rule rule NN cord-026306-mkmrninv 90 15 ( ( -LRB- cord-026306-mkmrninv 90 16 1 1 CD cord-026306-mkmrninv 90 17 ) ) -RRB- cord-026306-mkmrninv 90 18 is be VBZ cord-026306-mkmrninv 90 19 not not RB cord-026306-mkmrninv 90 20 applicable applicable JJ cord-026306-mkmrninv 90 21 in in IN cord-026306-mkmrninv 90 22 this this DT cord-026306-mkmrninv 90 23 case case NN cord-026306-mkmrninv 90 24 . . . cord-026306-mkmrninv 91 1 Another another DT cord-026306-mkmrninv 91 2 combination combination NN cord-026306-mkmrninv 91 3 technique technique NN cord-026306-mkmrninv 91 4 that that WDT cord-026306-mkmrninv 91 5 is be VBZ cord-026306-mkmrninv 91 6 similar similar JJ cord-026306-mkmrninv 91 7 to to IN cord-026306-mkmrninv 91 8 Demster Demster NNP cord-026306-mkmrninv 91 9 rule rule NN cord-026306-mkmrninv 91 10 is be VBZ cord-026306-mkmrninv 91 11 Yager Yager NNP cord-026306-mkmrninv 91 12 combination combination NN cord-026306-mkmrninv 91 13 rule rule NN cord-026306-mkmrninv 91 14 [ [ -LRB- cord-026306-mkmrninv 91 15 21 21 CD cord-026306-mkmrninv 91 16 ] ] -RRB- cord-026306-mkmrninv 91 17 that that WDT cord-026306-mkmrninv 91 18 is be VBZ cord-026306-mkmrninv 91 19 defined define VBN cord-026306-mkmrninv 91 20 as as IN cord-026306-mkmrninv 91 21 According accord VBG cord-026306-mkmrninv 91 22 to to IN cord-026306-mkmrninv 91 23 this this DT cord-026306-mkmrninv 91 24 rule rule NN cord-026306-mkmrninv 91 25 , , , cord-026306-mkmrninv 91 26 the the DT cord-026306-mkmrninv 91 27 value value NN cord-026306-mkmrninv 91 28 of of IN cord-026306-mkmrninv 91 29 conflict conflict NN cord-026306-mkmrninv 91 30 K k NN cord-026306-mkmrninv 91 31 is be VBZ cord-026306-mkmrninv 91 32 reallocated reallocate VBN cord-026306-mkmrninv 91 33 among among IN cord-026306-mkmrninv 91 34 the the DT cord-026306-mkmrninv 91 35 mass mass NN cord-026306-mkmrninv 91 36 of of IN cord-026306-mkmrninv 91 37 ignorance ignorance NN cord-026306-mkmrninv 91 38 m(X m(x ADD cord-026306-mkmrninv 91 39 ) ) -RRB- cord-026306-mkmrninv 91 40 . . . cord-026306-mkmrninv 92 1 Other other JJ cord-026306-mkmrninv 92 2 combination combination NN cord-026306-mkmrninv 92 3 rules rule NNS cord-026306-mkmrninv 92 4 are be VBP cord-026306-mkmrninv 92 5 also also RB cord-026306-mkmrninv 92 6 described describe VBN cord-026306-mkmrninv 92 7 in in IN cord-026306-mkmrninv 92 8 [ [ -LRB- cord-026306-mkmrninv 92 9 22 22 CD cord-026306-mkmrninv 92 10 ] ] -RRB- cord-026306-mkmrninv 92 11 , , , cord-026306-mkmrninv 92 12 some some DT cord-026306-mkmrninv 92 13 generalizations generalization NNS cord-026306-mkmrninv 92 14 can can MD cord-026306-mkmrninv 92 15 be be VB cord-026306-mkmrninv 92 16 found find VBN cord-026306-mkmrninv 92 17 in in IN cord-026306-mkmrninv 92 18 [ [ -LRB- cord-026306-mkmrninv 92 19 23 23 CD cord-026306-mkmrninv 92 20 , , , cord-026306-mkmrninv 92 21 24 24 CD cord-026306-mkmrninv 92 22 ] ] -RRB- cord-026306-mkmrninv 92 23 , , , cord-026306-mkmrninv 92 24 axiomatics axiomatic NNS cord-026306-mkmrninv 92 25 and and CC cord-026306-mkmrninv 92 26 the the DT cord-026306-mkmrninv 92 27 description description NN cord-026306-mkmrninv 92 28 of of IN cord-026306-mkmrninv 92 29 conflict conflict NN cord-026306-mkmrninv 92 30 rules rule NNS cord-026306-mkmrninv 92 31 are be VBP cord-026306-mkmrninv 92 32 reviewed review VBN cord-026306-mkmrninv 92 33 in in IN cord-026306-mkmrninv 92 34 [ [ -LRB- cord-026306-mkmrninv 92 35 25 25 CD cord-026306-mkmrninv 92 36 ] ] -RRB- cord-026306-mkmrninv 93 1 [ [ -LRB- cord-026306-mkmrninv 93 2 26 26 CD cord-026306-mkmrninv 93 3 ] ] -RRB- cord-026306-mkmrninv 94 1 [ [ -LRB- cord-026306-mkmrninv 94 2 27 27 CD cord-026306-mkmrninv 94 3 ] ] -RRB- cord-026306-mkmrninv 94 4 [ [ -LRB- cord-026306-mkmrninv 94 5 28 28 CD cord-026306-mkmrninv 94 6 ] ] -RRB- cord-026306-mkmrninv 94 7 . . . cord-026306-mkmrninv 95 1 Additionally additionally RB cord-026306-mkmrninv 95 2 , , , cord-026306-mkmrninv 95 3 discounted discount VBN cord-026306-mkmrninv 95 4 technique technique NN cord-026306-mkmrninv 95 5 proposed propose VBN cord-026306-mkmrninv 95 6 in in IN cord-026306-mkmrninv 95 7 [ [ -LRB- cord-026306-mkmrninv 95 8 1 1 CD cord-026306-mkmrninv 95 9 ] ] -RRB- cord-026306-mkmrninv 95 10 can can MD cord-026306-mkmrninv 95 11 be be VB cord-026306-mkmrninv 95 12 applied apply VBN cord-026306-mkmrninv 95 13 to to IN cord-026306-mkmrninv 95 14 mass mass JJ cord-026306-mkmrninv 95 15 functions function NNS cord-026306-mkmrninv 95 16 in in IN cord-026306-mkmrninv 95 17 case case NN cord-026306-mkmrninv 95 18 when when WRB cord-026306-mkmrninv 95 19 various various JJ cord-026306-mkmrninv 95 20 sources source NNS cord-026306-mkmrninv 95 21 of of IN cord-026306-mkmrninv 95 22 information information NN cord-026306-mkmrninv 95 23 that that WDT cord-026306-mkmrninv 95 24 are be VBP cord-026306-mkmrninv 95 25 determined determine VBN cord-026306-mkmrninv 95 26 by by IN cord-026306-mkmrninv 95 27 their -PRON- PRP$ cord-026306-mkmrninv 95 28 belief belief NN cord-026306-mkmrninv 95 29 functions function NNS cord-026306-mkmrninv 95 30 have have VBP cord-026306-mkmrninv 95 31 different different JJ cord-026306-mkmrninv 95 32 levels level NNS cord-026306-mkmrninv 95 33 of of IN cord-026306-mkmrninv 95 34 reliability reliability NN cord-026306-mkmrninv 95 35 or or CC cord-026306-mkmrninv 95 36 different different JJ cord-026306-mkmrninv 95 37 priority priority NN cord-026306-mkmrninv 95 38 . . . cord-026306-mkmrninv 96 1 Discounting discount VBG cord-026306-mkmrninv 96 2 of of IN cord-026306-mkmrninv 96 3 mass mass NN cord-026306-mkmrninv 96 4 functions function NNS cord-026306-mkmrninv 96 5 can can MD cord-026306-mkmrninv 96 6 be be VB cord-026306-mkmrninv 96 7 performed perform VBN cord-026306-mkmrninv 96 8 with with IN cord-026306-mkmrninv 96 9 the the DT cord-026306-mkmrninv 96 10 help help NN cord-026306-mkmrninv 96 11 of of IN cord-026306-mkmrninv 96 12 parameter parameter NN cord-026306-mkmrninv 96 13 α α NN cord-026306-mkmrninv 96 14 ∈ ∈ NN cord-026306-mkmrninv 96 15 [ [ -LRB- cord-026306-mkmrninv 96 16 0 0 CD cord-026306-mkmrninv 96 17 ; ; : cord-026306-mkmrninv 96 18 1 1 CD cord-026306-mkmrninv 96 19 ] ] -RRB- cord-026306-mkmrninv 96 20 as as IN cord-026306-mkmrninv 96 21 follows follow VBZ cord-026306-mkmrninv 96 22 : : : cord-026306-mkmrninv 97 1 If if IN cord-026306-mkmrninv 97 2 α α NN cord-026306-mkmrninv 97 3 = = SYM cord-026306-mkmrninv 97 4 0 0 NFP cord-026306-mkmrninv 97 5 then then RB cord-026306-mkmrninv 97 6 the the DT cord-026306-mkmrninv 97 7 source source NN cord-026306-mkmrninv 97 8 of of IN cord-026306-mkmrninv 97 9 information information NN cord-026306-mkmrninv 97 10 is be VBZ cord-026306-mkmrninv 97 11 regarded regard VBN cord-026306-mkmrninv 97 12 as as IN cord-026306-mkmrninv 97 13 thoroughly thoroughly RB cord-026306-mkmrninv 97 14 reliable reliable JJ cord-026306-mkmrninv 97 15 and and CC cord-026306-mkmrninv 97 16 m m NNP cord-026306-mkmrninv 97 17 α α NN cord-026306-mkmrninv 97 18 ( ( -LRB- cord-026306-mkmrninv 97 19 A a NN cord-026306-mkmrninv 97 20 ) ) -RRB- cord-026306-mkmrninv 98 1 = = SYM cord-026306-mkmrninv 98 2 m(A m(a LS cord-026306-mkmrninv 98 3 ) ) -RRB- cord-026306-mkmrninv 98 4 ∀A ∀A . cord-026306-mkmrninv 98 5 ∈ ∈ NN cord-026306-mkmrninv 98 6 2 2 CD cord-026306-mkmrninv 98 7 X x NN cord-026306-mkmrninv 98 8 . . . cord-026306-mkmrninv 99 1 Conversely conversely RB cord-026306-mkmrninv 99 2 , , , cord-026306-mkmrninv 99 3 if if IN cord-026306-mkmrninv 99 4 α α NN cord-026306-mkmrninv 99 5 = = SYM cord-026306-mkmrninv 99 6 1 1 CD cord-026306-mkmrninv 99 7 then then RB cord-026306-mkmrninv 99 8 m m NNP cord-026306-mkmrninv 99 9 α α NNP cord-026306-mkmrninv 99 10 ( ( -LRB- cord-026306-mkmrninv 99 11 X X NNP cord-026306-mkmrninv 99 12 ) ) -RRB- cord-026306-mkmrninv 99 13 = = SYM cord-026306-mkmrninv 99 14 1 1 CD cord-026306-mkmrninv 99 15 and and CC cord-026306-mkmrninv 99 16 the the DT cord-026306-mkmrninv 99 17 related related JJ cord-026306-mkmrninv 99 18 belief belief NN cord-026306-mkmrninv 99 19 function function NN cord-026306-mkmrninv 99 20 is be VBZ cord-026306-mkmrninv 99 21 vacuous vacuous JJ cord-026306-mkmrninv 99 22 . . . cord-026306-mkmrninv 100 1 In in IN cord-026306-mkmrninv 100 2 this this DT cord-026306-mkmrninv 100 3 Section section NN cord-026306-mkmrninv 100 4 we -PRON- PRP cord-026306-mkmrninv 100 5 describe describe VBP cord-026306-mkmrninv 100 6 a a DT cord-026306-mkmrninv 100 7 graph graph NN cord-026306-mkmrninv 100 8 model model NN cord-026306-mkmrninv 100 9 with with IN cord-026306-mkmrninv 100 10 one one CD cord-026306-mkmrninv 100 11 layer layer NN cord-026306-mkmrninv 100 12 of of IN cord-026306-mkmrninv 100 13 interaction interaction NN cord-026306-mkmrninv 100 14 as as RB cord-026306-mkmrninv 100 15 well well RB cord-026306-mkmrninv 100 16 as as IN cord-026306-mkmrninv 100 17 the the DT cord-026306-mkmrninv 100 18 construction construction NN cord-026306-mkmrninv 100 19 of of IN cord-026306-mkmrninv 100 20 centrality centrality NN cord-026306-mkmrninv 100 21 measure measure NN cord-026306-mkmrninv 100 22 based base VBN cord-026306-mkmrninv 100 23 on on IN cord-026306-mkmrninv 100 24 a a DT cord-026306-mkmrninv 100 25 mass mass JJ cord-026306-mkmrninv 100 26 function function NN cord-026306-mkmrninv 100 27 for for IN cord-026306-mkmrninv 100 28 a a DT cord-026306-mkmrninv 100 29 network network NN cord-026306-mkmrninv 100 30 . . . cord-026306-mkmrninv 101 1 We -PRON- PRP cord-026306-mkmrninv 101 2 consider consider VBP cord-026306-mkmrninv 101 3 connected connect VBN cord-026306-mkmrninv 101 4 graph graph NN cord-026306-mkmrninv 101 5 as as IN cord-026306-mkmrninv 101 6 tuple tuple NN cord-026306-mkmrninv 101 7 G g NN cord-026306-mkmrninv 101 8 = = : cord-026306-mkmrninv 101 9 ( ( -LRB- cord-026306-mkmrninv 101 10 V v NN cord-026306-mkmrninv 101 11 , , , cord-026306-mkmrninv 101 12 E E NNP cord-026306-mkmrninv 101 13 , , , cord-026306-mkmrninv 101 14 W W NNP cord-026306-mkmrninv 101 15 ) ) -RRB- cord-026306-mkmrninv 101 16 , , , cord-026306-mkmrninv 101 17 where where WRB cord-026306-mkmrninv 101 18 V v NN cord-026306-mkmrninv 101 19 = = NN cord-026306-mkmrninv 101 20 { { -LRB- cord-026306-mkmrninv 101 21 v v NN cord-026306-mkmrninv 101 22 1 1 CD cord-026306-mkmrninv 101 23 , , , cord-026306-mkmrninv 101 24 ... ... NFP cord-026306-mkmrninv 101 25 , , , cord-026306-mkmrninv 101 26 v v NN cord-026306-mkmrninv 101 27 n n NN cord-026306-mkmrninv 101 28 } } -RRB- cord-026306-mkmrninv 101 29 is be VBZ cord-026306-mkmrninv 101 30 a a DT cord-026306-mkmrninv 101 31 set set NN cord-026306-mkmrninv 101 32 of of IN cord-026306-mkmrninv 101 33 nodes node NNS cord-026306-mkmrninv 101 34 , , , cord-026306-mkmrninv 101 35 |V |v CD cord-026306-mkmrninv 101 36 | | NNP cord-026306-mkmrninv 101 37 = = SYM cord-026306-mkmrninv 101 38 n n NN cord-026306-mkmrninv 101 39 , , , cord-026306-mkmrninv 101 40 and and CC cord-026306-mkmrninv 101 41 E e NN cord-026306-mkmrninv 101 42 = = NN cord-026306-mkmrninv 101 43 { { -LRB- cord-026306-mkmrninv 102 1 e(v e(v NNP cord-026306-mkmrninv 102 2 i i PRP cord-026306-mkmrninv 102 3 , , , cord-026306-mkmrninv 102 4 v v NNP cord-026306-mkmrninv 102 5 j j NNP cord-026306-mkmrninv 102 6 ) ) -RRB- cord-026306-mkmrninv 102 7 } } -RRB- cord-026306-mkmrninv 102 8 as as IN cord-026306-mkmrninv 102 9 a a DT cord-026306-mkmrninv 102 10 set set NN cord-026306-mkmrninv 102 11 of of IN cord-026306-mkmrninv 102 12 edges edge NNS cord-026306-mkmrninv 102 13 . . . cord-026306-mkmrninv 103 1 For for IN cord-026306-mkmrninv 103 2 the the DT cord-026306-mkmrninv 103 3 simplicity simplicity NN cord-026306-mkmrninv 103 4 , , , cord-026306-mkmrninv 103 5 we -PRON- PRP cord-026306-mkmrninv 103 6 associate associate VBP cord-026306-mkmrninv 103 7 v v NN cord-026306-mkmrninv 103 8 k k NNP cord-026306-mkmrninv 103 9 with with IN cord-026306-mkmrninv 103 10 number number NN cord-026306-mkmrninv 103 11 k k NNP cord-026306-mkmrninv 103 12 , , , cord-026306-mkmrninv 103 13 k k NNP cord-026306-mkmrninv 103 14 = = SYM cord-026306-mkmrninv 103 15 1 1 CD cord-026306-mkmrninv 103 16 , , , cord-026306-mkmrninv 103 17 ... ... NFP cord-026306-mkmrninv 103 18 , , , cord-026306-mkmrninv 103 19 n n NN cord-026306-mkmrninv 103 20 and and CC cord-026306-mkmrninv 103 21 denote denote VB cord-026306-mkmrninv 103 22 e(v e(v NNP cord-026306-mkmrninv 103 23 i i NN cord-026306-mkmrninv 103 24 , , , cord-026306-mkmrninv 103 25 v v NNP cord-026306-mkmrninv 103 26 j j NNP cord-026306-mkmrninv 103 27 ) ) -RRB- cord-026306-mkmrninv 103 28 as as IN cord-026306-mkmrninv 103 29 e e NNP cord-026306-mkmrninv 103 30 ij ij NN cord-026306-mkmrninv 103 31 . . . cord-026306-mkmrninv 104 1 In in IN cord-026306-mkmrninv 104 2 this this DT cord-026306-mkmrninv 104 3 work work NN cord-026306-mkmrninv 104 4 we -PRON- PRP cord-026306-mkmrninv 104 5 consider consider VBP cord-026306-mkmrninv 104 6 undirected undirected JJ cord-026306-mkmrninv 104 7 network network NN cord-026306-mkmrninv 104 8 , , , cord-026306-mkmrninv 104 9 i.e. i.e. FW cord-026306-mkmrninv 104 10 e e FW cord-026306-mkmrninv 104 11 ij ij NN cord-026306-mkmrninv 104 12 ∈ ∈ NN cord-026306-mkmrninv 104 13 E E NNP cord-026306-mkmrninv 104 14 implies imply VBZ cord-026306-mkmrninv 104 15 that that IN cord-026306-mkmrninv 104 16 e e NN cord-026306-mkmrninv 104 17 ji ji NNP cord-026306-mkmrninv 104 18 ∈ ∈ NNP cord-026306-mkmrninv 105 1 E. E. NNP cord-026306-mkmrninv 105 2 We -PRON- PRP cord-026306-mkmrninv 105 3 also also RB cord-026306-mkmrninv 105 4 analyze analyze VBP cord-026306-mkmrninv 105 5 weighted weighted JJ cord-026306-mkmrninv 105 6 networks network NNS cord-026306-mkmrninv 105 7 , , , cord-026306-mkmrninv 105 8 i.e. i.e. FW cord-026306-mkmrninv 105 9 each each DT cord-026306-mkmrninv 105 10 edge edge NN cord-026306-mkmrninv 105 11 e e NN cord-026306-mkmrninv 105 12 ij ij NN cord-026306-mkmrninv 105 13 in in IN cord-026306-mkmrninv 105 14 network network NN cord-026306-mkmrninv 105 15 G G NNP cord-026306-mkmrninv 105 16 associates associate NNS cord-026306-mkmrninv 105 17 with with IN cord-026306-mkmrninv 105 18 weight weight NN cord-026306-mkmrninv 106 1 w w NNP cord-026306-mkmrninv 106 2 ij ij NNP cord-026306-mkmrninv 106 3 ∈ ∈ NNP cord-026306-mkmrninv 106 4 W W NNP cord-026306-mkmrninv 106 5 . . . cord-026306-mkmrninv 107 1 Without without IN cord-026306-mkmrninv 107 2 loss loss NN cord-026306-mkmrninv 107 3 of of IN cord-026306-mkmrninv 107 4 generality generality NN cord-026306-mkmrninv 107 5 , , , cord-026306-mkmrninv 107 6 we -PRON- PRP cord-026306-mkmrninv 107 7 assume assume VBP cord-026306-mkmrninv 107 8 that that IN cord-026306-mkmrninv 107 9 all all DT cord-026306-mkmrninv 107 10 weights weight NNS cord-026306-mkmrninv 107 11 w w NNP cord-026306-mkmrninv 107 12 ij ij NN cord-026306-mkmrninv 107 13 ∈ ∈ NNP cord-026306-mkmrninv 107 14 [ [ -LRB- cord-026306-mkmrninv 107 15 0 0 NFP cord-026306-mkmrninv 107 16 ; ; : cord-026306-mkmrninv 107 17 1 1 CD cord-026306-mkmrninv 107 18 ] ] -RRB- cord-026306-mkmrninv 107 19 and and CC cord-026306-mkmrninv 107 20 w w NNP cord-026306-mkmrninv 107 21 ij ij NN cord-026306-mkmrninv 107 22 = = SYM cord-026306-mkmrninv 107 23 0 0 CD cord-026306-mkmrninv 107 24 implies imply VBZ cord-026306-mkmrninv 107 25 that that IN cord-026306-mkmrninv 107 26 e e NN cord-026306-mkmrninv 107 27 ij ij NN cord-026306-mkmrninv 107 28 ∈ ∈ NNP cord-026306-mkmrninv 107 29 E. E. NNP cord-026306-mkmrninv 107 30 Weight Weight NNP cord-026306-mkmrninv 107 31 w w NNP cord-026306-mkmrninv 107 32 ij ij NN cord-026306-mkmrninv 107 33 between between IN cord-026306-mkmrninv 107 34 nodes node NNS cord-026306-mkmrninv 107 35 v v IN cord-026306-mkmrninv 107 36 i i PRP cord-026306-mkmrninv 107 37 and and CC cord-026306-mkmrninv 107 38 v v NNP cord-026306-mkmrninv 107 39 j j NNP cord-026306-mkmrninv 107 40 indicates indicate VBZ cord-026306-mkmrninv 107 41 the the DT cord-026306-mkmrninv 107 42 degree degree NN cord-026306-mkmrninv 107 43 of of IN cord-026306-mkmrninv 107 44 interaction interaction NN cord-026306-mkmrninv 107 45 between between IN cord-026306-mkmrninv 107 46 corresponding correspond VBG cord-026306-mkmrninv 107 47 nodes node NNS cord-026306-mkmrninv 107 48 . . . cord-026306-mkmrninv 108 1 Our -PRON- PRP$ cord-026306-mkmrninv 108 2 main main JJ cord-026306-mkmrninv 108 3 focus focus NN cord-026306-mkmrninv 108 4 is be VBZ cord-026306-mkmrninv 108 5 to to TO cord-026306-mkmrninv 108 6 range range VB cord-026306-mkmrninv 108 7 nodes node NNS cord-026306-mkmrninv 108 8 with with IN cord-026306-mkmrninv 108 9 respect respect NN cord-026306-mkmrninv 108 10 their -PRON- PRP$ cord-026306-mkmrninv 108 11 importance importance NN cord-026306-mkmrninv 108 12 in in IN cord-026306-mkmrninv 108 13 a a DT cord-026306-mkmrninv 108 14 network network NN cord-026306-mkmrninv 108 15 . . . cord-026306-mkmrninv 109 1 We -PRON- PRP cord-026306-mkmrninv 109 2 assume assume VBP cord-026306-mkmrninv 109 3 that that IN cord-026306-mkmrninv 109 4 a a DT cord-026306-mkmrninv 109 5 node node NN cord-026306-mkmrninv 109 6 is be VBZ cord-026306-mkmrninv 109 7 considered consider VBN cord-026306-mkmrninv 109 8 to to TO cord-026306-mkmrninv 109 9 be be VB cord-026306-mkmrninv 109 10 pivotal pivotal JJ cord-026306-mkmrninv 109 11 if if IN cord-026306-mkmrninv 109 12 it -PRON- PRP cord-026306-mkmrninv 109 13 actively actively RB cord-026306-mkmrninv 109 14 interacts interact VBZ cord-026306-mkmrninv 109 15 with with IN cord-026306-mkmrninv 109 16 other other JJ cord-026306-mkmrninv 109 17 nodes node NNS cord-026306-mkmrninv 109 18 in in IN cord-026306-mkmrninv 109 19 a a DT cord-026306-mkmrninv 109 20 graph graph NN cord-026306-mkmrninv 109 21 . . . cord-026306-mkmrninv 110 1 In in IN cord-026306-mkmrninv 110 2 our -PRON- PRP$ cord-026306-mkmrninv 110 3 analysis analysis NN cord-026306-mkmrninv 110 4 we -PRON- PRP cord-026306-mkmrninv 110 5 take take VBP cord-026306-mkmrninv 110 6 into into IN cord-026306-mkmrninv 110 7 account account NN cord-026306-mkmrninv 110 8 the the DT cord-026306-mkmrninv 110 9 connections connection NNS cord-026306-mkmrninv 110 10 with with IN cord-026306-mkmrninv 110 11 distant distant JJ cord-026306-mkmrninv 110 12 nodes node NNS cord-026306-mkmrninv 110 13 as as RB cord-026306-mkmrninv 110 14 well well RB cord-026306-mkmrninv 110 15 as as IN cord-026306-mkmrninv 110 16 the the DT cord-026306-mkmrninv 110 17 cooperation cooperation NN cord-026306-mkmrninv 110 18 with with IN cord-026306-mkmrninv 110 19 group group NN cord-026306-mkmrninv 110 20 of of IN cord-026306-mkmrninv 110 21 other other JJ cord-026306-mkmrninv 110 22 nodes node NNS cord-026306-mkmrninv 110 23 . . . cord-026306-mkmrninv 111 1 More more RBR cord-026306-mkmrninv 111 2 precisely precisely RB cord-026306-mkmrninv 111 3 , , , cord-026306-mkmrninv 111 4 we -PRON- PRP cord-026306-mkmrninv 111 5 suppose suppose VBP cord-026306-mkmrninv 111 6 that that IN cord-026306-mkmrninv 111 7 centrality centrality NN cord-026306-mkmrninv 111 8 of of IN cord-026306-mkmrninv 111 9 a a DT cord-026306-mkmrninv 111 10 node node NN cord-026306-mkmrninv 111 11 depends depend VBZ cord-026306-mkmrninv 111 12 on on IN cord-026306-mkmrninv 111 13 relative relative JJ cord-026306-mkmrninv 111 14 aggregated aggregated JJ cord-026306-mkmrninv 111 15 weight weight NN cord-026306-mkmrninv 111 16 of of IN cord-026306-mkmrninv 111 17 adjacent adjacent JJ cord-026306-mkmrninv 111 18 subgraphs subgraphs NN cord-026306-mkmrninv 111 19 to to IN cord-026306-mkmrninv 111 20 the the DT cord-026306-mkmrninv 111 21 considered consider VBN cord-026306-mkmrninv 111 22 node node NN cord-026306-mkmrninv 111 23 . . . cord-026306-mkmrninv 112 1 At at IN cord-026306-mkmrninv 112 2 the the DT cord-026306-mkmrninv 112 3 same same JJ cord-026306-mkmrninv 112 4 time time NN cord-026306-mkmrninv 112 5 , , , cord-026306-mkmrninv 112 6 the the DT cord-026306-mkmrninv 112 7 aggregated aggregated JJ cord-026306-mkmrninv 112 8 weight weight NN cord-026306-mkmrninv 112 9 of of IN cord-026306-mkmrninv 112 10 a a DT cord-026306-mkmrninv 112 11 subgraph subgraph NN cord-026306-mkmrninv 112 12 can can MD cord-026306-mkmrninv 112 13 be be VB cord-026306-mkmrninv 112 14 estimated estimate VBN cord-026306-mkmrninv 112 15 with with IN cord-026306-mkmrninv 112 16 the the DT cord-026306-mkmrninv 112 17 help help NN cord-026306-mkmrninv 112 18 of of IN cord-026306-mkmrninv 112 19 monotonic monotonic JJ cord-026306-mkmrninv 112 20 measures measure NNS cord-026306-mkmrninv 112 21 including include VBG cord-026306-mkmrninv 112 22 such such JJ cord-026306-mkmrninv 112 23 measures measure NNS cord-026306-mkmrninv 112 24 as as IN cord-026306-mkmrninv 112 25 belief belief NN cord-026306-mkmrninv 112 26 functions function NNS cord-026306-mkmrninv 112 27 . . . cord-026306-mkmrninv 113 1 We -PRON- PRP cord-026306-mkmrninv 113 2 consider consider VBP cord-026306-mkmrninv 113 3 a a DT cord-026306-mkmrninv 113 4 family family NN cord-026306-mkmrninv 113 5 of of IN cord-026306-mkmrninv 113 6 belief belief NN cord-026306-mkmrninv 113 7 functions function NNS cord-026306-mkmrninv 113 8 We -PRON- PRP cord-026306-mkmrninv 113 9 denote denote VBP cord-026306-mkmrninv 113 10 by by IN cord-026306-mkmrninv 113 11 |W |w CD cord-026306-mkmrninv 113 12 | | NNS cord-026306-mkmrninv 114 1 = = NFP cord-026306-mkmrninv 115 1 i i PRP cord-026306-mkmrninv 116 1 < < NNP cord-026306-mkmrninv 116 2 j j NNP cord-026306-mkmrninv 116 3 w w NNP cord-026306-mkmrninv 116 4 ij ij NNP cord-026306-mkmrninv 117 1 the the DT cord-026306-mkmrninv 117 2 total total JJ cord-026306-mkmrninv 117 3 sum sum NN cord-026306-mkmrninv 117 4 of of IN cord-026306-mkmrninv 117 5 all all DT cord-026306-mkmrninv 117 6 weights weight NNS cord-026306-mkmrninv 117 7 in in IN cord-026306-mkmrninv 117 8 a a DT cord-026306-mkmrninv 117 9 graph graph NN cord-026306-mkmrninv 117 10 . . . cord-026306-mkmrninv 118 1 Next next RB cord-026306-mkmrninv 118 2 , , , cord-026306-mkmrninv 118 3 we -PRON- PRP cord-026306-mkmrninv 118 4 define define VBP cord-026306-mkmrninv 118 5 mass mass NN cord-026306-mkmrninv 118 6 function function NN cord-026306-mkmrninv 118 7 m m NNP cord-026306-mkmrninv 118 8 k k NNP cord-026306-mkmrninv 118 9 of of IN cord-026306-mkmrninv 118 10 node node NN cord-026306-mkmrninv 118 11 v v NNP cord-026306-mkmrninv 118 12 k k NNP cord-026306-mkmrninv 118 13 in in IN cord-026306-mkmrninv 118 14 connected connected JJ cord-026306-mkmrninv 118 15 graph graph NN cord-026306-mkmrninv 118 16 G g NN cord-026306-mkmrninv 118 17 as as IN cord-026306-mkmrninv 118 18 follows follow VBZ cord-026306-mkmrninv 118 19 : : : cord-026306-mkmrninv 118 20 where where WRB cord-026306-mkmrninv 118 21 N N NNP cord-026306-mkmrninv 118 22 is be VBZ cord-026306-mkmrninv 118 23 a a DT cord-026306-mkmrninv 118 24 discount discount NN cord-026306-mkmrninv 118 25 factor factor NN cord-026306-mkmrninv 118 26 that that WDT cord-026306-mkmrninv 118 27 decreases decrease VBZ cord-026306-mkmrninv 118 28 the the DT cord-026306-mkmrninv 118 29 importance importance NN cord-026306-mkmrninv 118 30 of of IN cord-026306-mkmrninv 118 31 the the DT cord-026306-mkmrninv 118 32 connection connection NN cord-026306-mkmrninv 118 33 of of IN cord-026306-mkmrninv 118 34 node node NN cord-026306-mkmrninv 118 35 v v NNP cord-026306-mkmrninv 118 36 k k NN cord-026306-mkmrninv 118 37 with with IN cord-026306-mkmrninv 118 38 distant distant JJ cord-026306-mkmrninv 118 39 nodes node NNS cord-026306-mkmrninv 118 40 . . . cord-026306-mkmrninv 119 1 This this DT cord-026306-mkmrninv 119 2 coefficient coefficient NN cord-026306-mkmrninv 119 3 can can MD cord-026306-mkmrninv 119 4 be be VB cord-026306-mkmrninv 119 5 determined determine VBN cord-026306-mkmrninv 119 6 in in IN cord-026306-mkmrninv 119 7 the the DT cord-026306-mkmrninv 119 8 following following JJ cord-026306-mkmrninv 119 9 way way NN cord-026306-mkmrninv 119 10 : : : cord-026306-mkmrninv 119 11 where where WRB cord-026306-mkmrninv 119 12 d d NNP cord-026306-mkmrninv 119 13 is be VBZ cord-026306-mkmrninv 119 14 a a DT cord-026306-mkmrninv 119 15 distance distance NN cord-026306-mkmrninv 119 16 between between IN cord-026306-mkmrninv 119 17 corresponding correspond VBG cord-026306-mkmrninv 119 18 nodes node NNS cord-026306-mkmrninv 119 19 . . . cord-026306-mkmrninv 120 1 A a DT cord-026306-mkmrninv 120 2 mass mass JJ cord-026306-mkmrninv 120 3 function function NN cord-026306-mkmrninv 120 4 of of IN cord-026306-mkmrninv 120 5 the the DT cord-026306-mkmrninv 120 6 k k XX cord-026306-mkmrninv 120 7 - - HYPH cord-026306-mkmrninv 120 8 th th XX cord-026306-mkmrninv 120 9 node node NN cord-026306-mkmrninv 120 10 reaches reach VBZ cord-026306-mkmrninv 120 11 the the DT cord-026306-mkmrninv 120 12 higher high JJR cord-026306-mkmrninv 120 13 values value NNS cord-026306-mkmrninv 120 14 on on IN cord-026306-mkmrninv 120 15 single single JJ cord-026306-mkmrninv 120 16 nodes node NNS cord-026306-mkmrninv 120 17 that that WDT cord-026306-mkmrninv 120 18 are be VBP cord-026306-mkmrninv 120 19 adjacent adjacent JJ cord-026306-mkmrninv 120 20 to to IN cord-026306-mkmrninv 120 21 the the DT cord-026306-mkmrninv 120 22 k k NN cord-026306-mkmrninv 120 23 - - HYPH cord-026306-mkmrninv 120 24 th th XX cord-026306-mkmrninv 120 25 node node NN cord-026306-mkmrninv 120 26 and and CC cord-026306-mkmrninv 120 27 the the DT cord-026306-mkmrninv 120 28 lower low JJR cord-026306-mkmrninv 120 29 values value NNS cord-026306-mkmrninv 120 30 on on IN cord-026306-mkmrninv 120 31 the the DT cord-026306-mkmrninv 120 32 pairs pair NNS cord-026306-mkmrninv 120 33 of of IN cord-026306-mkmrninv 120 34 connected connected JJ cord-026306-mkmrninv 120 35 nodes node NNS cord-026306-mkmrninv 120 36 that that IN cord-026306-mkmrninv 120 37 both both DT cord-026306-mkmrninv 120 38 belongs belong VBZ cord-026306-mkmrninv 120 39 to to IN cord-026306-mkmrninv 120 40 the the DT cord-026306-mkmrninv 120 41 p p NN cord-026306-mkmrninv 120 42 - - HYPH cord-026306-mkmrninv 120 43 neighborhood neighborhood NN cord-026306-mkmrninv 120 44 of of IN cord-026306-mkmrninv 120 45 node node NNP cord-026306-mkmrninv 120 46 k. k. NNP cord-026306-mkmrninv 121 1 Thus thus RB cord-026306-mkmrninv 121 2 , , , cord-026306-mkmrninv 121 3 the the DT cord-026306-mkmrninv 121 4 value value NN cord-026306-mkmrninv 121 5 of of IN cord-026306-mkmrninv 121 6 mass mass NN cord-026306-mkmrninv 121 7 function function NN cord-026306-mkmrninv 121 8 ( ( -LRB- cord-026306-mkmrninv 121 9 3 3 CD cord-026306-mkmrninv 121 10 ) ) -RRB- cord-026306-mkmrninv 121 11 on on IN cord-026306-mkmrninv 121 12 one one CD cord-026306-mkmrninv 121 13 - - HYPH cord-026306-mkmrninv 121 14 and and CC cord-026306-mkmrninv 121 15 twoelement twoelement NN cord-026306-mkmrninv 121 16 sets set NNS cord-026306-mkmrninv 121 17 is be VBZ cord-026306-mkmrninv 121 18 proportional proportional JJ cord-026306-mkmrninv 121 19 to to IN cord-026306-mkmrninv 121 20 the the DT cord-026306-mkmrninv 121 21 weights weight NNS cord-026306-mkmrninv 121 22 on on IN cord-026306-mkmrninv 121 23 corresponding correspond VBG cord-026306-mkmrninv 121 24 edges edge NNS cord-026306-mkmrninv 121 25 and and CC cord-026306-mkmrninv 121 26 inversely inversely RB cord-026306-mkmrninv 121 27 proportional proportional JJ cord-026306-mkmrninv 121 28 to to IN cord-026306-mkmrninv 121 29 the the DT cord-026306-mkmrninv 121 30 distance distance NN cord-026306-mkmrninv 121 31 to to IN cord-026306-mkmrninv 121 32 a a DT cord-026306-mkmrninv 121 33 considered consider VBN cord-026306-mkmrninv 121 34 node node NN cord-026306-mkmrninv 121 35 . . . cord-026306-mkmrninv 122 1 Belief belief NN cord-026306-mkmrninv 122 2 function function NN cord-026306-mkmrninv 123 1 g g NNP cord-026306-mkmrninv 123 2 k k NNP cord-026306-mkmrninv 123 3 aggregates aggregate VBZ cord-026306-mkmrninv 123 4 the the DT cord-026306-mkmrninv 123 5 obtained obtain VBN cord-026306-mkmrninv 123 6 mass mass NN cord-026306-mkmrninv 123 7 functions function NNS cord-026306-mkmrninv 123 8 and and CC cord-026306-mkmrninv 123 9 corresponding correspond VBG cord-026306-mkmrninv 123 10 weights weight NNS cord-026306-mkmrninv 123 11 over over IN cord-026306-mkmrninv 123 12 all all DT cord-026306-mkmrninv 123 13 nodes node NNS cord-026306-mkmrninv 123 14 and and CC cord-026306-mkmrninv 123 15 edges edge NNS cord-026306-mkmrninv 123 16 that that WDT cord-026306-mkmrninv 123 17 are be VBP cord-026306-mkmrninv 123 18 contained contain VBN cord-026306-mkmrninv 123 19 in in IN cord-026306-mkmrninv 123 20 p p NN cord-026306-mkmrninv 123 21 - - HYPH cord-026306-mkmrninv 123 22 neighborhood neighborhood NN cord-026306-mkmrninv 123 23 of of IN cord-026306-mkmrninv 123 24 the the DT cord-026306-mkmrninv 123 25 k k XX cord-026306-mkmrninv 123 26 - - HYPH cord-026306-mkmrninv 123 27 th th XX cord-026306-mkmrninv 123 28 node node NN cord-026306-mkmrninv 123 29 . . . cord-026306-mkmrninv 124 1 Other other JJ cord-026306-mkmrninv 124 2 characteristics characteristic NNS cord-026306-mkmrninv 124 3 can can MD cord-026306-mkmrninv 124 4 be be VB cord-026306-mkmrninv 124 5 also also RB cord-026306-mkmrninv 124 6 taken take VBN cord-026306-mkmrninv 124 7 into into IN cord-026306-mkmrninv 124 8 account account NN cord-026306-mkmrninv 124 9 as as IN cord-026306-mkmrninv 124 10 weighted weighted JJ cord-026306-mkmrninv 124 11 path path NN cord-026306-mkmrninv 124 12 between between IN cord-026306-mkmrninv 124 13 nodes node NNS cord-026306-mkmrninv 124 14 , , , cord-026306-mkmrninv 124 15 the the DT cord-026306-mkmrninv 124 16 joint joint JJ cord-026306-mkmrninv 124 17 intensity intensity NN cord-026306-mkmrninv 124 18 of of IN cord-026306-mkmrninv 124 19 the the DT cord-026306-mkmrninv 124 20 connections connection NNS cord-026306-mkmrninv 124 21 along along IN cord-026306-mkmrninv 124 22 the the DT cord-026306-mkmrninv 124 23 considered consider VBN cord-026306-mkmrninv 124 24 path path NN cord-026306-mkmrninv 124 25 , , , cord-026306-mkmrninv 124 26 etc etc FW cord-026306-mkmrninv 124 27 . . . cord-026306-mkmrninv 125 1 It -PRON- PRP cord-026306-mkmrninv 125 2 can can MD cord-026306-mkmrninv 125 3 be be VB cord-026306-mkmrninv 125 4 seen see VBN cord-026306-mkmrninv 125 5 that that IN cord-026306-mkmrninv 125 6 the the DT cord-026306-mkmrninv 125 7 proposed propose VBN cord-026306-mkmrninv 125 8 mass mass NN cord-026306-mkmrninv 125 9 function function NN cord-026306-mkmrninv 125 10 m m NNP cord-026306-mkmrninv 125 11 k k NN cord-026306-mkmrninv 126 1 : : : cord-026306-mkmrninv 126 2 2 2 CD cord-026306-mkmrninv 126 3 V v NN cord-026306-mkmrninv 126 4 → → NN cord-026306-mkmrninv 126 5 [ [ -LRB- cord-026306-mkmrninv 126 6 0 0 CD cord-026306-mkmrninv 126 7 ; ; : cord-026306-mkmrninv 126 8 1 1 LS cord-026306-mkmrninv 126 9 ] ] -RRB- cord-026306-mkmrninv 126 10 satisfies satisfy VBZ cord-026306-mkmrninv 126 11 the the DT cord-026306-mkmrninv 126 12 normalization normalization NN cord-026306-mkmrninv 126 13 condition condition NN cord-026306-mkmrninv 126 14 : : : cord-026306-mkmrninv 126 15 m m NNP cord-026306-mkmrninv 126 16 k k NNP cord-026306-mkmrninv 126 17 ( ( -LRB- cord-026306-mkmrninv 126 18 ∅ ∅ NNP cord-026306-mkmrninv 126 19 ) ) -RRB- cord-026306-mkmrninv 126 20 = = SYM cord-026306-mkmrninv 126 21 0 0 CD cord-026306-mkmrninv 126 22 , , , cord-026306-mkmrninv 127 1 A∈2 A∈2 NNP cord-026306-mkmrninv 128 1 V v NN cord-026306-mkmrninv 128 2 m m NN cord-026306-mkmrninv 129 1 k k NNP cord-026306-mkmrninv 129 2 ( ( -LRB- cord-026306-mkmrninv 129 3 A a NN cord-026306-mkmrninv 129 4 ) ) -RRB- cord-026306-mkmrninv 129 5 = = SYM cord-026306-mkmrninv 129 6 1 1 CD cord-026306-mkmrninv 129 7 . . . cord-026306-mkmrninv 130 1 Thus thus RB cord-026306-mkmrninv 130 2 , , , cord-026306-mkmrninv 130 3 we -PRON- PRP cord-026306-mkmrninv 130 4 can can MD cord-026306-mkmrninv 130 5 regard regard VB cord-026306-mkmrninv 130 6 m m NNP cord-026306-mkmrninv 130 7 k k NNP cord-026306-mkmrninv 130 8 as as IN cord-026306-mkmrninv 130 9 basic basic JJ cord-026306-mkmrninv 130 10 probability probability NN cord-026306-mkmrninv 130 11 assignments assignment NNS cord-026306-mkmrninv 130 12 and and CC cord-026306-mkmrninv 130 13 g g NN cord-026306-mkmrninv 130 14 k k NN cord-026306-mkmrninv 130 15 = = NN cord-026306-mkmrninv 130 16 B b NN cord-026306-mkmrninv 130 17 m m NN cord-026306-mkmrninv 130 18 k k NN cord-026306-mkmrninv 130 19 ( ( -LRB- cord-026306-mkmrninv 130 20 B)η B)η NNP cord-026306-mkmrninv 130 21 B B NNP cord-026306-mkmrninv 130 22 are be VBP cord-026306-mkmrninv 130 23 belief belief NN cord-026306-mkmrninv 130 24 functions function NNS cord-026306-mkmrninv 130 25 of of IN cord-026306-mkmrninv 130 26 V v NN cord-026306-mkmrninv 130 27 . . . cord-026306-mkmrninv 131 1 Similar similar JJ cord-026306-mkmrninv 131 2 measures measure NNS cord-026306-mkmrninv 131 3 for for IN cord-026306-mkmrninv 131 4 the the DT cord-026306-mkmrninv 131 5 nodes node NNS cord-026306-mkmrninv 131 6 influence influence VBP cord-026306-mkmrninv 131 7 assessment assessment NN cord-026306-mkmrninv 131 8 in in IN cord-026306-mkmrninv 131 9 networks network NNS cord-026306-mkmrninv 131 10 are be VBP cord-026306-mkmrninv 131 11 proposed propose VBN cord-026306-mkmrninv 131 12 in in IN cord-026306-mkmrninv 131 13 [ [ -LRB- cord-026306-mkmrninv 131 14 29 29 CD cord-026306-mkmrninv 131 15 ] ] -RRB- cord-026306-mkmrninv 131 16 . . . cord-026306-mkmrninv 132 1 The the DT cord-026306-mkmrninv 132 2 proposed propose VBN cord-026306-mkmrninv 132 3 mass mass NN cord-026306-mkmrninv 132 4 function function NN cord-026306-mkmrninv 132 5 m m NNP cord-026306-mkmrninv 132 6 k k NNP cord-026306-mkmrninv 132 7 ( ( -LRB- cord-026306-mkmrninv 132 8 A a NN cord-026306-mkmrninv 132 9 ) ) -RRB- cord-026306-mkmrninv 132 10 characterizes characterize VBZ cord-026306-mkmrninv 132 11 the the DT cord-026306-mkmrninv 132 12 distribution distribution NN cord-026306-mkmrninv 132 13 of of IN cord-026306-mkmrninv 132 14 pure pure JJ cord-026306-mkmrninv 132 15 interaction interaction NN cord-026306-mkmrninv 132 16 of of IN cord-026306-mkmrninv 132 17 node node NN cord-026306-mkmrninv 132 18 v v NNP cord-026306-mkmrninv 132 19 k k NNP cord-026306-mkmrninv 132 20 with with IN cord-026306-mkmrninv 132 21 a a DT cord-026306-mkmrninv 132 22 set set NN cord-026306-mkmrninv 132 23 of of IN cord-026306-mkmrninv 132 24 closely closely RB cord-026306-mkmrninv 132 25 located locate VBN cord-026306-mkmrninv 132 26 nodes node NNS cord-026306-mkmrninv 132 27 from from IN cord-026306-mkmrninv 132 28 A a DT cord-026306-mkmrninv 132 29 , , , cord-026306-mkmrninv 132 30 i.e. i.e. FW cord-026306-mkmrninv 132 31 we -PRON- PRP cord-026306-mkmrninv 132 32 exclude exclude VBP cord-026306-mkmrninv 132 33 the the DT cord-026306-mkmrninv 132 34 interactions interaction NNS cord-026306-mkmrninv 132 35 with with IN cord-026306-mkmrninv 132 36 other other JJ cord-026306-mkmrninv 132 37 subsets subset NNS cord-026306-mkmrninv 132 38 of of IN cord-026306-mkmrninv 132 39 A a NN cord-026306-mkmrninv 132 40 in in IN cord-026306-mkmrninv 132 41 m m NNP cord-026306-mkmrninv 132 42 k k NN cord-026306-mkmrninv 132 43 ( ( -LRB- cord-026306-mkmrninv 132 44 A A NNP cord-026306-mkmrninv 132 45 ) ) -RRB- cord-026306-mkmrninv 132 46 . . . cord-026306-mkmrninv 133 1 The the DT cord-026306-mkmrninv 133 2 value value NN cord-026306-mkmrninv 133 3 m m NNP cord-026306-mkmrninv 133 4 k k NN cord-026306-mkmrninv 133 5 ( ( -LRB- cord-026306-mkmrninv 133 6 V V NNP cord-026306-mkmrninv 133 7 ) ) -RRB- cord-026306-mkmrninv 133 8 indicates indicate VBZ cord-026306-mkmrninv 133 9 the the DT cord-026306-mkmrninv 133 10 level level NN cord-026306-mkmrninv 133 11 of of IN cord-026306-mkmrninv 133 12 ignorance ignorance NN cord-026306-mkmrninv 133 13 of of IN cord-026306-mkmrninv 133 14 the the DT cord-026306-mkmrninv 133 15 interactions interaction NNS cord-026306-mkmrninv 133 16 between between IN cord-026306-mkmrninv 133 17 node node NN cord-026306-mkmrninv 133 18 v v NNP cord-026306-mkmrninv 133 19 k k NN cord-026306-mkmrninv 133 20 and and CC cord-026306-mkmrninv 133 21 distant distant JJ cord-026306-mkmrninv 133 22 nodes node NNS cord-026306-mkmrninv 133 23 in in IN cord-026306-mkmrninv 133 24 the the DT cord-026306-mkmrninv 133 25 graph graph NN cord-026306-mkmrninv 133 26 outside outside IN cord-026306-mkmrninv 133 27 N n CD cord-026306-mkmrninv 134 1 ( ( -LRB- cord-026306-mkmrninv 134 2 p p NN cord-026306-mkmrninv 134 3 ) ) -RRB- cord-026306-mkmrninv 134 4 k k NN cord-026306-mkmrninv 134 5 . . . cord-026306-mkmrninv 135 1 The the DT cord-026306-mkmrninv 135 2 pairwise pairwise JJ cord-026306-mkmrninv 135 3 interaction interaction NN cord-026306-mkmrninv 135 4 between between IN cord-026306-mkmrninv 135 5 nodes node NNS cord-026306-mkmrninv 135 6 can can MD cord-026306-mkmrninv 135 7 be be VB cord-026306-mkmrninv 135 8 estimated estimate VBN cord-026306-mkmrninv 135 9 by by IN cord-026306-mkmrninv 135 10 the the DT cord-026306-mkmrninv 135 11 reallocation reallocation NN cord-026306-mkmrninv 135 12 of of IN cord-026306-mkmrninv 135 13 m m NNP cord-026306-mkmrninv 135 14 k k NNP cord-026306-mkmrninv 135 15 ( ( -LRB- cord-026306-mkmrninv 135 16 A A NNP cord-026306-mkmrninv 135 17 ) ) -RRB- cord-026306-mkmrninv 135 18 among among IN cord-026306-mkmrninv 135 19 all all DT cord-026306-mkmrninv 135 20 nodes node NNS cord-026306-mkmrninv 135 21 in in IN cord-026306-mkmrninv 135 22 A. a. NN cord-026306-mkmrninv 136 1 This this DT cord-026306-mkmrninv 136 2 can can MD cord-026306-mkmrninv 136 3 be be VB cord-026306-mkmrninv 136 4 done do VBN cord-026306-mkmrninv 136 5 with with IN cord-026306-mkmrninv 136 6 the the DT cord-026306-mkmrninv 136 7 help help NN cord-026306-mkmrninv 136 8 of of IN cord-026306-mkmrninv 136 9 so so RB cord-026306-mkmrninv 136 10 - - HYPH cord-026306-mkmrninv 136 11 called call VBN cord-026306-mkmrninv 136 12 pignistic pignistic JJ cord-026306-mkmrninv 136 13 probabilities probability NNS cord-026306-mkmrninv 136 14 proposed propose VBN cord-026306-mkmrninv 136 15 in in IN cord-026306-mkmrninv 136 16 [ [ -LRB- cord-026306-mkmrninv 136 17 30 30 CD cord-026306-mkmrninv 136 18 ] ] -RRB- cord-026306-mkmrninv 136 19 : : : cord-026306-mkmrninv 136 20 It -PRON- PRP cord-026306-mkmrninv 136 21 has have VBZ cord-026306-mkmrninv 136 22 been be VBN cord-026306-mkmrninv 136 23 known know VBN cord-026306-mkmrninv 136 24 that that IN cord-026306-mkmrninv 136 25 pignistic pignistic JJ cord-026306-mkmrninv 136 26 probabilities probability NNS cord-026306-mkmrninv 136 27 for for IN cord-026306-mkmrninv 136 28 belief belief NN cord-026306-mkmrninv 136 29 function function NN cord-026306-mkmrninv 137 1 g g NN cord-026306-mkmrninv 137 2 k k NN cord-026306-mkmrninv 137 3 = = NN cord-026306-mkmrninv 137 4 B b NN cord-026306-mkmrninv 137 5 m m NN cord-026306-mkmrninv 137 6 k k NN cord-026306-mkmrninv 138 1 ( ( -LRB- cord-026306-mkmrninv 138 2 B)η B)η NNP cord-026306-mkmrninv 138 3 B B NNP cord-026306-mkmrninv 138 4 defined define VBN cord-026306-mkmrninv 138 5 on on IN cord-026306-mkmrninv 138 6 V v NN cord-026306-mkmrninv 138 7 coincide coincide NN cord-026306-mkmrninv 138 8 with with IN cord-026306-mkmrninv 138 9 Shapley shapley JJ cord-026306-mkmrninv 138 10 values value NNS cord-026306-mkmrninv 138 11 [ [ -LRB- cord-026306-mkmrninv 138 12 31 31 CD cord-026306-mkmrninv 138 13 ] ] -RRB- cord-026306-mkmrninv 138 14 that that WDT cord-026306-mkmrninv 138 15 are be VBP cord-026306-mkmrninv 138 16 widely widely RB cord-026306-mkmrninv 138 17 used use VBN cord-026306-mkmrninv 138 18 in in IN cord-026306-mkmrninv 138 19 cooperative cooperative JJ cord-026306-mkmrninv 138 20 game game NN cord-026306-mkmrninv 138 21 theory theory NN cord-026306-mkmrninv 138 22 and and CC cord-026306-mkmrninv 138 23 are be VBP cord-026306-mkmrninv 138 24 calculated calculate VBN cord-026306-mkmrninv 138 25 as as IN cord-026306-mkmrninv 138 26 follows follow VBZ cord-026306-mkmrninv 138 27 : : : cord-026306-mkmrninv 139 1 Value value NN cord-026306-mkmrninv 139 2 Bet Bet NNP cord-026306-mkmrninv 139 3 v v NN cord-026306-mkmrninv 139 4 k k NN cord-026306-mkmrninv 140 1 ( ( -LRB- cord-026306-mkmrninv 140 2 { { -LRB- cord-026306-mkmrninv 140 3 u u NN cord-026306-mkmrninv 140 4 } } -RRB- cord-026306-mkmrninv 140 5 ) ) -RRB- cord-026306-mkmrninv 140 6 indicates indicate VBZ cord-026306-mkmrninv 140 7 the the DT cord-026306-mkmrninv 140 8 fraction fraction NN cord-026306-mkmrninv 140 9 of of IN cord-026306-mkmrninv 140 10 interaction interaction NN cord-026306-mkmrninv 140 11 of of IN cord-026306-mkmrninv 140 12 node node NN cord-026306-mkmrninv 140 13 v v NNP cord-026306-mkmrninv 140 14 k k NNP cord-026306-mkmrninv 140 15 with with IN cord-026306-mkmrninv 140 16 node node NN cord-026306-mkmrninv 140 17 u. u. NNP cord-026306-mkmrninv 140 18 Hence Hence NNP cord-026306-mkmrninv 140 19 , , , cord-026306-mkmrninv 140 20 the the DT cord-026306-mkmrninv 140 21 value value NN cord-026306-mkmrninv 140 22 shows show VBZ cord-026306-mkmrninv 140 23 the the DT cord-026306-mkmrninv 140 24 total total JJ cord-026306-mkmrninv 140 25 cooperation cooperation NN cord-026306-mkmrninv 140 26 with with IN cord-026306-mkmrninv 140 27 node node NN cord-026306-mkmrninv 140 28 v v NN cord-026306-mkmrninv 140 29 in in IN cord-026306-mkmrninv 140 30 graph graph NN cord-026306-mkmrninv 141 1 G. G. NNP cord-026306-mkmrninv 141 2 Consequently consequently RB cord-026306-mkmrninv 141 3 , , , cord-026306-mkmrninv 141 4 the the DT cord-026306-mkmrninv 141 5 ranking ranking NN cord-026306-mkmrninv 141 6 of of IN cord-026306-mkmrninv 141 7 q q NNP cord-026306-mkmrninv 141 8 values value NNS cord-026306-mkmrninv 141 9 demonstrates demonstrate VBZ cord-026306-mkmrninv 141 10 the the DT cord-026306-mkmrninv 141 11 importance importance NN cord-026306-mkmrninv 141 12 on on IN cord-026306-mkmrninv 141 13 nodes node NNS cord-026306-mkmrninv 141 14 with with IN cord-026306-mkmrninv 141 15 respect respect NN cord-026306-mkmrninv 141 16 to to IN cord-026306-mkmrninv 141 17 their -PRON- PRP$ cord-026306-mkmrninv 141 18 activity activity NN cord-026306-mkmrninv 141 19 in in IN cord-026306-mkmrninv 141 20 the the DT cord-026306-mkmrninv 141 21 considered consider VBN cord-026306-mkmrninv 141 22 graph graph NN cord-026306-mkmrninv 141 23 . . . cord-026306-mkmrninv 142 1 We -PRON- PRP cord-026306-mkmrninv 142 2 also also RB cord-026306-mkmrninv 142 3 note note VBP cord-026306-mkmrninv 142 4 that that IN cord-026306-mkmrninv 142 5 if if IN cord-026306-mkmrninv 142 6 graph graph NN cord-026306-mkmrninv 142 7 G G NNP cord-026306-mkmrninv 142 8 has have VBZ cord-026306-mkmrninv 142 9 several several JJ cord-026306-mkmrninv 142 10 connected connect VBN cord-026306-mkmrninv 142 11 components component NNS cord-026306-mkmrninv 142 12 then then RB cord-026306-mkmrninv 142 13 the the DT cord-026306-mkmrninv 142 14 proposed propose VBN cord-026306-mkmrninv 142 15 analysis analysis NN cord-026306-mkmrninv 142 16 is be VBZ cord-026306-mkmrninv 142 17 provided provide VBN cord-026306-mkmrninv 142 18 for for IN cord-026306-mkmrninv 142 19 each each DT cord-026306-mkmrninv 142 20 component component NN cord-026306-mkmrninv 142 21 separately separately RB cord-026306-mkmrninv 142 22 . . . cord-026306-mkmrninv 143 1 The the DT cord-026306-mkmrninv 143 2 size size NN cord-026306-mkmrninv 143 3 of of IN cord-026306-mkmrninv 143 4 each each DT cord-026306-mkmrninv 143 5 component component NN cord-026306-mkmrninv 143 6 can can MD cord-026306-mkmrninv 143 7 be be VB cord-026306-mkmrninv 143 8 taken take VBN cord-026306-mkmrninv 143 9 into into IN cord-026306-mkmrninv 143 10 account account NN cord-026306-mkmrninv 143 11 in in IN cord-026306-mkmrninv 143 12 order order NN cord-026306-mkmrninv 143 13 not not RB cord-026306-mkmrninv 143 14 to to TO cord-026306-mkmrninv 143 15 overestimate overestimate VB cord-026306-mkmrninv 143 16 the the DT cord-026306-mkmrninv 143 17 interactions interaction NNS cord-026306-mkmrninv 143 18 in in IN cord-026306-mkmrninv 143 19 small small JJ cord-026306-mkmrninv 143 20 groups group NNS cord-026306-mkmrninv 143 21 . . . cord-026306-mkmrninv 144 1 We -PRON- PRP cord-026306-mkmrninv 144 2 illustrate illustrate VBP cord-026306-mkmrninv 144 3 the the DT cord-026306-mkmrninv 144 4 proposed propose VBN cord-026306-mkmrninv 144 5 model model NN cord-026306-mkmrninv 144 6 on on IN cord-026306-mkmrninv 144 7 a a DT cord-026306-mkmrninv 144 8 toy toy NN cord-026306-mkmrninv 144 9 example example NN cord-026306-mkmrninv 144 10 represented represent VBN cord-026306-mkmrninv 144 11 on on IN cord-026306-mkmrninv 144 12 Fig Fig NNP cord-026306-mkmrninv 144 13 . . . cord-026306-mkmrninv 145 1 1 1 LS cord-026306-mkmrninv 145 2 . . . cord-026306-mkmrninv 146 1 For for IN cord-026306-mkmrninv 146 2 the the DT cord-026306-mkmrninv 146 3 graph graph NN cord-026306-mkmrninv 146 4 on on IN cord-026306-mkmrninv 146 5 Fig Fig NNP cord-026306-mkmrninv 146 6 . . . cord-026306-mkmrninv 146 7 1 1 CD cord-026306-mkmrninv 146 8 _SP cord-026306-mkmrninv 147 1 The the DT cord-026306-mkmrninv 147 2 same same JJ cord-026306-mkmrninv 147 3 ranking ranking NN cord-026306-mkmrninv 147 4 can can MD cord-026306-mkmrninv 147 5 be be VB cord-026306-mkmrninv 147 6 obtained obtain VBN cord-026306-mkmrninv 147 7 with with IN cord-026306-mkmrninv 147 8 eigenvector eigenvector NN cord-026306-mkmrninv 147 9 centrality centrality NN cord-026306-mkmrninv 147 10 measure measure NN cord-026306-mkmrninv 147 11 , , , cord-026306-mkmrninv 147 12 which which WDT cord-026306-mkmrninv 147 13 confirms confirm VBZ cord-026306-mkmrninv 147 14 the the DT cord-026306-mkmrninv 147 15 consistency consistency NN cord-026306-mkmrninv 147 16 of of IN cord-026306-mkmrninv 147 17 the the DT cord-026306-mkmrninv 147 18 proposed propose VBN cord-026306-mkmrninv 147 19 approach approach NN cord-026306-mkmrninv 147 20 . . . cord-026306-mkmrninv 148 1 It -PRON- PRP cord-026306-mkmrninv 148 2 can can MD cord-026306-mkmrninv 148 3 be be VB cord-026306-mkmrninv 148 4 also also RB cord-026306-mkmrninv 148 5 proved prove VBN cord-026306-mkmrninv 148 6 that that IN cord-026306-mkmrninv 148 7 if if IN cord-026306-mkmrninv 148 8 we -PRON- PRP cord-026306-mkmrninv 148 9 consider consider VBP cord-026306-mkmrninv 148 10 a a DT cord-026306-mkmrninv 148 11 1-neighborhood 1-neighborhood CD cord-026306-mkmrninv 148 12 of of IN cord-026306-mkmrninv 148 13 a a DT cord-026306-mkmrninv 148 14 node node NN cord-026306-mkmrninv 148 15 that that IN cord-026306-mkmrninv 148 16 , , , cord-026306-mkmrninv 148 17 in in IN cord-026306-mkmrninv 148 18 its -PRON- PRP$ cord-026306-mkmrninv 148 19 turn turn NN cord-026306-mkmrninv 148 20 , , , cord-026306-mkmrninv 148 21 induces induce VBZ cord-026306-mkmrninv 148 22 an an DT cord-026306-mkmrninv 148 23 acyclic acyclic JJ cord-026306-mkmrninv 148 24 subgraph subgraph NN cord-026306-mkmrninv 148 25 ( ( -LRB- cord-026306-mkmrninv 148 26 i.e. i.e. FW cord-026306-mkmrninv 148 27 a a DT cord-026306-mkmrninv 148 28 star star NN cord-026306-mkmrninv 148 29 subgraph subgraph NN cord-026306-mkmrninv 148 30 ) ) -RRB- cord-026306-mkmrninv 149 1 then then RB cord-026306-mkmrninv 149 2 the the DT cord-026306-mkmrninv 149 3 centrality centrality NN cord-026306-mkmrninv 149 4 value value NN cord-026306-mkmrninv 149 5 of of IN cord-026306-mkmrninv 149 6 a a DT cord-026306-mkmrninv 149 7 node node NN cord-026306-mkmrninv 149 8 according accord VBG cord-026306-mkmrninv 149 9 to to IN cord-026306-mkmrninv 149 10 formulas formula NNS cord-026306-mkmrninv 149 11 ( ( -LRB- cord-026306-mkmrninv 149 12 3)-(6 3)-(6 CD cord-026306-mkmrninv 149 13 ) ) -RRB- cord-026306-mkmrninv 149 14 is be VBZ cord-026306-mkmrninv 149 15 associated associate VBN cord-026306-mkmrninv 149 16 with with IN cord-026306-mkmrninv 149 17 a a DT cord-026306-mkmrninv 149 18 degree degree NN cord-026306-mkmrninv 149 19 centrality centrality NN cord-026306-mkmrninv 149 20 measure measure NN cord-026306-mkmrninv 149 21 . . . cord-026306-mkmrninv 150 1 More more RBR cord-026306-mkmrninv 150 2 precisely precisely RB cord-026306-mkmrninv 150 3 , , , cord-026306-mkmrninv 150 4 it -PRON- PRP cord-026306-mkmrninv 150 5 can can MD cord-026306-mkmrninv 150 6 be be VB cord-026306-mkmrninv 150 7 formulated formulate VBN cord-026306-mkmrninv 150 8 as as IN cord-026306-mkmrninv 150 9 follows follow VBZ cord-026306-mkmrninv 150 10 . . . cord-026306-mkmrninv 150 11 _SP cord-026306-mkmrninv 151 1 where where WRB cord-026306-mkmrninv 151 2 n(v n(v NNP cord-026306-mkmrninv 151 3 ) ) -RRB- cord-026306-mkmrninv 152 1 = = NFP cord-026306-mkmrninv 153 1 u u LS cord-026306-mkmrninv 153 2 : : : cord-026306-mkmrninv 153 3 e(v e(v NNP cord-026306-mkmrninv 153 4 , , , cord-026306-mkmrninv 153 5 u)∈E u)∈E NNP cord-026306-mkmrninv 153 6 w(v w(v NNP cord-026306-mkmrninv 153 7 , , , cord-026306-mkmrninv 153 8 u u NNP cord-026306-mkmrninv 153 9 ) ) -RRB- cord-026306-mkmrninv 153 10 is be VBZ cord-026306-mkmrninv 153 11 a a DT cord-026306-mkmrninv 153 12 weighted weighted JJ cord-026306-mkmrninv 153 13 degree degree NN cord-026306-mkmrninv 153 14 of of IN cord-026306-mkmrninv 153 15 node node NN cord-026306-mkmrninv 153 16 v v NNP cord-026306-mkmrninv 153 17 , , , cord-026306-mkmrninv 153 18 n n NN cord-026306-mkmrninv 153 19 = = SYM cord-026306-mkmrninv 153 20 |V |v CD cord-026306-mkmrninv 153 21 | | NNP cord-026306-mkmrninv 153 22 . . . cord-026306-mkmrninv 154 1 According accord VBG cord-026306-mkmrninv 154 2 to to IN cord-026306-mkmrninv 154 3 Proposition Proposition NNP cord-026306-mkmrninv 154 4 1 1 CD cord-026306-mkmrninv 154 5 , , , cord-026306-mkmrninv 154 6 the the DT cord-026306-mkmrninv 154 7 interaction interaction NN cord-026306-mkmrninv 154 8 centrality centrality NN cord-026306-mkmrninv 154 9 value value NN cord-026306-mkmrninv 154 10 q q NNP cord-026306-mkmrninv 154 11 v v NN cord-026306-mkmrninv 154 12 constructed construct VBN cord-026306-mkmrninv 154 13 via via IN cord-026306-mkmrninv 154 14 belief belief NN cord-026306-mkmrninv 154 15 functions function NNS cord-026306-mkmrninv 154 16 is be VBZ cord-026306-mkmrninv 154 17 proportional proportional JJ cord-026306-mkmrninv 154 18 to to IN cord-026306-mkmrninv 154 19 weighted weighted JJ cord-026306-mkmrninv 154 20 degree degree NN cord-026306-mkmrninv 154 21 centrality centrality NN cord-026306-mkmrninv 154 22 of of IN cord-026306-mkmrninv 154 23 node node NN cord-026306-mkmrninv 154 24 v v LS cord-026306-mkmrninv 154 25 up up IN cord-026306-mkmrninv 154 26 to to IN cord-026306-mkmrninv 154 27 the the DT cord-026306-mkmrninv 154 28 constant constant JJ cord-026306-mkmrninv 154 29 term term NN cord-026306-mkmrninv 154 30 independent independent JJ cord-026306-mkmrninv 154 31 of of IN cord-026306-mkmrninv 154 32 node node NN cord-026306-mkmrninv 154 33 v v NN cord-026306-mkmrninv 154 34 with with IN cord-026306-mkmrninv 154 35 respect respect NN cord-026306-mkmrninv 154 36 to to IN cord-026306-mkmrninv 154 37 configuration configuration NN cord-026306-mkmrninv 154 38 described describe VBN cord-026306-mkmrninv 154 39 above above RB cord-026306-mkmrninv 154 40 . . . cord-026306-mkmrninv 155 1 In in IN cord-026306-mkmrninv 155 2 many many JJ cord-026306-mkmrninv 155 3 real real JJ cord-026306-mkmrninv 155 4 - - HYPH cord-026306-mkmrninv 155 5 world world NN cord-026306-mkmrninv 155 6 systems system NNS cord-026306-mkmrninv 155 7 the the DT cord-026306-mkmrninv 155 8 same same JJ cord-026306-mkmrninv 155 9 set set NN cord-026306-mkmrninv 155 10 of of IN cord-026306-mkmrninv 155 11 objects object NNS cord-026306-mkmrninv 155 12 can can MD cord-026306-mkmrninv 155 13 interact interact VB cord-026306-mkmrninv 155 14 with with IN cord-026306-mkmrninv 155 15 each each DT cord-026306-mkmrninv 155 16 other other JJ cord-026306-mkmrninv 155 17 in in IN cord-026306-mkmrninv 155 18 several several JJ cord-026306-mkmrninv 155 19 ways way NNS cord-026306-mkmrninv 155 20 . . . cord-026306-mkmrninv 156 1 Thus thus RB cord-026306-mkmrninv 156 2 , , , cord-026306-mkmrninv 156 3 an an DT cord-026306-mkmrninv 156 4 appropriate appropriate JJ cord-026306-mkmrninv 156 5 network network NN cord-026306-mkmrninv 156 6 model model NN cord-026306-mkmrninv 156 7 is be VBZ cord-026306-mkmrninv 156 8 required require VBN cord-026306-mkmrninv 156 9 in in IN cord-026306-mkmrninv 156 10 order order NN cord-026306-mkmrninv 156 11 to to TO cord-026306-mkmrninv 156 12 qualitatively qualitatively RB cord-026306-mkmrninv 156 13 analyze analyze VB cord-026306-mkmrninv 156 14 the the DT cord-026306-mkmrninv 156 15 relations relation NNS cord-026306-mkmrninv 156 16 between between IN cord-026306-mkmrninv 156 17 nodes node NNS cord-026306-mkmrninv 156 18 . . . cord-026306-mkmrninv 157 1 This this DT cord-026306-mkmrninv 157 2 can can MD cord-026306-mkmrninv 157 3 be be VB cord-026306-mkmrninv 157 4 done do VBN cord-026306-mkmrninv 157 5 with with IN cord-026306-mkmrninv 157 6 the the DT cord-026306-mkmrninv 157 7 help help NN cord-026306-mkmrninv 157 8 of of IN cord-026306-mkmrninv 157 9 a a DT cord-026306-mkmrninv 157 10 multiplex multiplex JJ cord-026306-mkmrninv 157 11 network network NN cord-026306-mkmrninv 157 12 that that WDT cord-026306-mkmrninv 157 13 represents represent VBZ cord-026306-mkmrninv 157 14 a a DT cord-026306-mkmrninv 157 15 system system NN cord-026306-mkmrninv 157 16 of of IN cord-026306-mkmrninv 157 17 graphs graph NNS cord-026306-mkmrninv 157 18 with with IN cord-026306-mkmrninv 157 19 many many JJ cord-026306-mkmrninv 157 20 layers layer NNS cord-026306-mkmrninv 157 21 of of IN cord-026306-mkmrninv 157 22 interaction interaction NN cord-026306-mkmrninv 157 23 . . . cord-026306-mkmrninv 158 1 The the DT cord-026306-mkmrninv 158 2 key key JJ cord-026306-mkmrninv 158 3 point point NN cord-026306-mkmrninv 158 4 here here RB cord-026306-mkmrninv 158 5 is be VBZ cord-026306-mkmrninv 158 6 that that IN cord-026306-mkmrninv 158 7 the the DT cord-026306-mkmrninv 158 8 whole whole JJ cord-026306-mkmrninv 158 9 system system NN cord-026306-mkmrninv 158 10 of of IN cord-026306-mkmrninv 158 11 graphs graph NNS cord-026306-mkmrninv 158 12 should should MD cord-026306-mkmrninv 158 13 be be VB cord-026306-mkmrninv 158 14 analyzed analyze VBN cord-026306-mkmrninv 158 15 jointly jointly RB cord-026306-mkmrninv 158 16 as as IN cord-026306-mkmrninv 158 17 a a DT cord-026306-mkmrninv 158 18 single single JJ cord-026306-mkmrninv 158 19 entity entity NN cord-026306-mkmrninv 158 20 . . . cord-026306-mkmrninv 159 1 Next next RB cord-026306-mkmrninv 159 2 , , , cord-026306-mkmrninv 159 3 we -PRON- PRP cord-026306-mkmrninv 159 4 describe describe VBP cord-026306-mkmrninv 159 5 a a DT cord-026306-mkmrninv 159 6 multiplex multiplex JJ cord-026306-mkmrninv 159 7 graph graph NN cord-026306-mkmrninv 159 8 model model NN cord-026306-mkmrninv 159 9 and and CC cord-026306-mkmrninv 159 10 the the DT cord-026306-mkmrninv 159 11 technique technique NN cord-026306-mkmrninv 159 12 for for IN cord-026306-mkmrninv 159 13 the the DT cord-026306-mkmrninv 159 14 assessment assessment NN cord-026306-mkmrninv 159 15 of of IN cord-026306-mkmrninv 159 16 important important JJ cord-026306-mkmrninv 159 17 elements element NNS cord-026306-mkmrninv 159 18 in in IN cord-026306-mkmrninv 159 19 such such JJ cord-026306-mkmrninv 159 20 systems system NNS cord-026306-mkmrninv 159 21 . . . cord-026306-mkmrninv 160 1 We -PRON- PRP cord-026306-mkmrninv 160 2 consider consider VBP cord-026306-mkmrninv 160 3 a a DT cord-026306-mkmrninv 160 4 multiplex multiplex JJ cord-026306-mkmrninv 160 5 graph graph NN cord-026306-mkmrninv 160 6 as as IN cord-026306-mkmrninv 160 7 the the DT cord-026306-mkmrninv 160 8 family family NN cord-026306-mkmrninv 160 9 of of IN cord-026306-mkmrninv 160 10 networks network NNS cord-026306-mkmrninv 160 11 G g NN cord-026306-mkmrninv 160 12 = = NFP cord-026306-mkmrninv 160 13 ( ( -LRB- cord-026306-mkmrninv 160 14 V v NN cord-026306-mkmrninv 160 15 , , , cord-026306-mkmrninv 160 16 E E NNP cord-026306-mkmrninv 160 17 ( ( -LRB- cord-026306-mkmrninv 160 18 s s NNP cord-026306-mkmrninv 160 19 ) ) -RRB- cord-026306-mkmrninv 160 20 , , , cord-026306-mkmrninv 160 21 W W NNP cord-026306-mkmrninv 160 22 ( ( -LRB- cord-026306-mkmrninv 160 23 s s NN cord-026306-mkmrninv 160 24 ) ) -RRB- cord-026306-mkmrninv 160 25 ) ) -RRB- cord-026306-mkmrninv 160 26 with with IN cord-026306-mkmrninv 160 27 the the DT cord-026306-mkmrninv 160 28 common common JJ cord-026306-mkmrninv 160 29 set set NN cord-026306-mkmrninv 160 30 of of IN cord-026306-mkmrninv 160 31 nodes node NNS cord-026306-mkmrninv 160 32 V v NN cord-026306-mkmrninv 160 33 = = NN cord-026306-mkmrninv 160 34 { { -LRB- cord-026306-mkmrninv 160 35 v v NN cord-026306-mkmrninv 160 36 1 1 CD cord-026306-mkmrninv 160 37 , , , cord-026306-mkmrninv 160 38 ... ... NFP cord-026306-mkmrninv 160 39 , , , cord-026306-mkmrninv 160 40 v v NN cord-026306-mkmrninv 160 41 n n NN cord-026306-mkmrninv 160 42 } } -RRB- cord-026306-mkmrninv 160 43 but but CC cord-026306-mkmrninv 160 44 distinct distinct JJ cord-026306-mkmrninv 160 45 set set NN cord-026306-mkmrninv 160 46 of of IN cord-026306-mkmrninv 160 47 edges edge NNS cord-026306-mkmrninv 160 48 .. .. NFP cord-026306-mkmrninv 160 49 , , , cord-026306-mkmrninv 160 50 l l NNP cord-026306-mkmrninv 160 51 } } -RRB- cord-026306-mkmrninv 160 52 indicates indicate VBZ cord-026306-mkmrninv 160 53 a a DT cord-026306-mkmrninv 160 54 particular particular JJ cord-026306-mkmrninv 160 55 network network NN cord-026306-mkmrninv 160 56 - - HYPH cord-026306-mkmrninv 160 57 layer layer NN cord-026306-mkmrninv 160 58 in in IN cord-026306-mkmrninv 160 59 a a DT cord-026306-mkmrninv 160 60 multiplex multiplex JJ cord-026306-mkmrninv 160 61 graph graph NN cord-026306-mkmrninv 160 62 with with IN cord-026306-mkmrninv 160 63 l l NN cord-026306-mkmrninv 160 64 levels level NNS cord-026306-mkmrninv 160 65 of of IN cord-026306-mkmrninv 160 66 interaction interaction NN cord-026306-mkmrninv 160 67 . . . cord-026306-mkmrninv 161 1 As as IN cord-026306-mkmrninv 161 2 it -PRON- PRP cord-026306-mkmrninv 161 3 is be VBZ cord-026306-mkmrninv 161 4 stated state VBN cord-026306-mkmrninv 161 5 above above RB cord-026306-mkmrninv 161 6 , , , cord-026306-mkmrninv 161 7 we -PRON- PRP cord-026306-mkmrninv 161 8 associate associate VBP cord-026306-mkmrninv 161 9 node node NN cord-026306-mkmrninv 161 10 v v NNP cord-026306-mkmrninv 161 11 k k NNP cord-026306-mkmrninv 161 12 with with IN cord-026306-mkmrninv 161 13 number number NN cord-026306-mkmrninv 161 14 k k NNP cord-026306-mkmrninv 161 15 , , , cord-026306-mkmrninv 161 16 k k NNP cord-026306-mkmrninv 161 17 = = SYM cord-026306-mkmrninv 161 18 1 1 CD cord-026306-mkmrninv 161 19 , , , cord-026306-mkmrninv 161 20 ... ... NFP cord-026306-mkmrninv 161 21 , , , cord-026306-mkmrninv 161 22 n n XX cord-026306-mkmrninv 161 23 and and CC cord-026306-mkmrninv 161 24 denote denote VB cord-026306-mkmrninv 161 25 e e NN cord-026306-mkmrninv 161 26 ( ( -LRB- cord-026306-mkmrninv 161 27 s s NN cord-026306-mkmrninv 161 28 ) ) -RRB- cord-026306-mkmrninv 161 29 ij ij NN cord-026306-mkmrninv 161 30 . . . cord-026306-mkmrninv 162 1 The the DT cord-026306-mkmrninv 162 2 other other JJ cord-026306-mkmrninv 162 3 notations notation NNS cord-026306-mkmrninv 162 4 remain remain VBP cord-026306-mkmrninv 162 5 the the DT cord-026306-mkmrninv 162 6 same same JJ cord-026306-mkmrninv 162 7 adjusted adjust VBN cord-026306-mkmrninv 162 8 to to TO cord-026306-mkmrninv 162 9 layer layer NN cord-026306-mkmrninv 162 10 s. s. NNP cord-026306-mkmrninv 163 1 In in IN cord-026306-mkmrninv 163 2 order order NN cord-026306-mkmrninv 163 3 to to TO cord-026306-mkmrninv 163 4 obtain obtain VB cord-026306-mkmrninv 163 5 central central JJ cord-026306-mkmrninv 163 6 elements element NNS cord-026306-mkmrninv 163 7 in in IN cord-026306-mkmrninv 163 8 the the DT cord-026306-mkmrninv 163 9 whole whole JJ cord-026306-mkmrninv 163 10 system system NN cord-026306-mkmrninv 163 11 we -PRON- PRP cord-026306-mkmrninv 163 12 can can MD cord-026306-mkmrninv 163 13 estimate estimate VB cord-026306-mkmrninv 163 14 the the DT cord-026306-mkmrninv 163 15 important important JJ cord-026306-mkmrninv 163 16 elements element NNS cord-026306-mkmrninv 163 17 at at IN cord-026306-mkmrninv 163 18 each each DT cord-026306-mkmrninv 163 19 layer layer NN cord-026306-mkmrninv 163 20 separately separately RB cord-026306-mkmrninv 163 21 , , , cord-026306-mkmrninv 163 22 for for IN cord-026306-mkmrninv 163 23 example example NN cord-026306-mkmrninv 163 24 , , , cord-026306-mkmrninv 163 25 with with IN cord-026306-mkmrninv 163 26 the the DT cord-026306-mkmrninv 163 27 help help NN cord-026306-mkmrninv 163 28 of of IN cord-026306-mkmrninv 163 29 the the DT cord-026306-mkmrninv 163 30 approach approach NN cord-026306-mkmrninv 163 31 described describe VBN cord-026306-mkmrninv 163 32 above above RB cord-026306-mkmrninv 163 33 . . . cord-026306-mkmrninv 164 1 As as IN cord-026306-mkmrninv 164 2 the the DT cord-026306-mkmrninv 164 3 result result NN cord-026306-mkmrninv 164 4 , , , cord-026306-mkmrninv 164 5 we -PRON- PRP cord-026306-mkmrninv 164 6 derive derive VBP cord-026306-mkmrninv 164 7 a a DT cord-026306-mkmrninv 164 8 family family NN cord-026306-mkmrninv 164 9 of of IN cord-026306-mkmrninv 164 10 vectors vector NNS cord-026306-mkmrninv 164 11 q q NNP cord-026306-mkmrninv 164 12 ( ( -LRB- cord-026306-mkmrninv 164 13 s s NN cord-026306-mkmrninv 164 14 ) ) -RRB- cord-026306-mkmrninv 164 15 that that WDT cord-026306-mkmrninv 164 16 can can MD cord-026306-mkmrninv 164 17 be be VB cord-026306-mkmrninv 164 18 aggregated aggregate VBN cord-026306-mkmrninv 164 19 into into IN cord-026306-mkmrninv 164 20 a a DT cord-026306-mkmrninv 164 21 single single JJ cord-026306-mkmrninv 164 22 ranking ranking NN cord-026306-mkmrninv 164 23 . . . cord-026306-mkmrninv 165 1 However however RB cord-026306-mkmrninv 165 2 , , , cord-026306-mkmrninv 165 3 we -PRON- PRP cord-026306-mkmrninv 165 4 consider consider VBP cord-026306-mkmrninv 165 5 all all DT cord-026306-mkmrninv 165 6 layers layer NNS cord-026306-mkmrninv 165 7 independently independently RB cord-026306-mkmrninv 165 8 of of IN cord-026306-mkmrninv 165 9 each each DT cord-026306-mkmrninv 165 10 other other JJ cord-026306-mkmrninv 165 11 , , , cord-026306-mkmrninv 165 12 which which WDT cord-026306-mkmrninv 165 13 means mean VBZ cord-026306-mkmrninv 165 14 that that IN cord-026306-mkmrninv 165 15 multiplex multiplex NN cord-026306-mkmrninv 165 16 system system NN cord-026306-mkmrninv 165 17 loses lose VBZ cord-026306-mkmrninv 165 18 its -PRON- PRP$ cord-026306-mkmrninv 165 19 significance significance NN cord-026306-mkmrninv 165 20 . . . cord-026306-mkmrninv 166 1 Instead instead RB cord-026306-mkmrninv 166 2 , , , cord-026306-mkmrninv 166 3 we -PRON- PRP cord-026306-mkmrninv 166 4 consider consider VBP cord-026306-mkmrninv 166 5 another another DT cord-026306-mkmrninv 166 6 approach approach NN cord-026306-mkmrninv 166 7 . . . cord-026306-mkmrninv 167 1 Firstly firstly RB cord-026306-mkmrninv 167 2 , , , cord-026306-mkmrninv 167 3 we -PRON- PRP cord-026306-mkmrninv 167 4 calculate calculate VBP cord-026306-mkmrninv 167 5 the the DT cord-026306-mkmrninv 167 6 set set NN cord-026306-mkmrninv 167 7 of of IN cord-026306-mkmrninv 167 8 mass mass NN cord-026306-mkmrninv 167 9 functions function NNS cord-026306-mkmrninv 167 10 m m NNP cord-026306-mkmrninv 167 11 for for IN cord-026306-mkmrninv 167 12 each each DT cord-026306-mkmrninv 167 13 layer layer NN cord-026306-mkmrninv 167 14 s s NN cord-026306-mkmrninv 167 15 , , , cord-026306-mkmrninv 167 16 s s NN cord-026306-mkmrninv 167 17 = = SYM cord-026306-mkmrninv 167 18 1 1 CD cord-026306-mkmrninv 167 19 , , , cord-026306-mkmrninv 167 20 ... ... NFP cord-026306-mkmrninv 167 21 , , , cord-026306-mkmrninv 168 1 l. l. NNP cord-026306-mkmrninv 168 2 Further further RB cord-026306-mkmrninv 168 3 , , , cord-026306-mkmrninv 168 4 this this DT cord-026306-mkmrninv 168 5 set set NN cord-026306-mkmrninv 168 6 can can MD cord-026306-mkmrninv 168 7 be be VB cord-026306-mkmrninv 168 8 put put VBN cord-026306-mkmrninv 168 9 together together RB cord-026306-mkmrninv 168 10 into into IN cord-026306-mkmrninv 168 11 an an DT cord-026306-mkmrninv 168 12 aggregated aggregated JJ cord-026306-mkmrninv 168 13 mass mass NN cord-026306-mkmrninv 168 14 function function NN cord-026306-mkmrninv 168 15 with with IN cord-026306-mkmrninv 168 16 the the DT cord-026306-mkmrninv 168 17 help help NN cord-026306-mkmrninv 168 18 of of IN cord-026306-mkmrninv 168 19 combination combination NN cord-026306-mkmrninv 168 20 rule rule NN cord-026306-mkmrninv 168 21 R r NN cord-026306-mkmrninv 168 22 as as IN cord-026306-mkmrninv 168 23 m m NNP cord-026306-mkmrninv 168 24 k k NN cord-026306-mkmrninv 168 25 = = SYM cord-026306-mkmrninv 168 26 m m NNP cord-026306-mkmrninv 168 27 k k NNP cord-026306-mkmrninv 168 28 . . . cord-026306-mkmrninv 169 1 Note note VB cord-026306-mkmrninv 169 2 that that IN cord-026306-mkmrninv 169 3 discounted discount VBD cord-026306-mkmrninv 169 4 coefficients coefficient NNS cord-026306-mkmrninv 169 5 α α NN cord-026306-mkmrninv 169 6 can can MD cord-026306-mkmrninv 169 7 be be VB cord-026306-mkmrninv 169 8 applied apply VBN cord-026306-mkmrninv 169 9 at at IN cord-026306-mkmrninv 169 10 this this DT cord-026306-mkmrninv 169 11 stage stage NN cord-026306-mkmrninv 169 12 as as RB cord-026306-mkmrninv 169 13 well well RB cord-026306-mkmrninv 169 14 . . . cord-026306-mkmrninv 170 1 Finally finally RB cord-026306-mkmrninv 170 2 , , , cord-026306-mkmrninv 170 3 we -PRON- PRP cord-026306-mkmrninv 170 4 can can MD cord-026306-mkmrninv 170 5 derive derive VB cord-026306-mkmrninv 170 6 centralities centrality NNS cord-026306-mkmrninv 170 7 for for IN cord-026306-mkmrninv 170 8 all all DT cord-026306-mkmrninv 170 9 elements element NNS cord-026306-mkmrninv 170 10 in in IN cord-026306-mkmrninv 170 11 the the DT cord-026306-mkmrninv 170 12 considered consider VBN cord-026306-mkmrninv 170 13 system system NN cord-026306-mkmrninv 170 14 as as IN cord-026306-mkmrninv 170 15 it -PRON- PRP cord-026306-mkmrninv 170 16 is be VBZ cord-026306-mkmrninv 170 17 described describe VBN cord-026306-mkmrninv 170 18 in in IN cord-026306-mkmrninv 170 19 formulas formula NNS cord-026306-mkmrninv 170 20 ( ( -LRB- cord-026306-mkmrninv 170 21 5 5 CD cord-026306-mkmrninv 170 22 ) ) -RRB- cord-026306-mkmrninv 170 23 and and CC cord-026306-mkmrninv 170 24 ( ( -LRB- cord-026306-mkmrninv 170 25 6 6 CD cord-026306-mkmrninv 170 26 ) ) -RRB- cord-026306-mkmrninv 170 27 . . . cord-026306-mkmrninv 171 1 In in IN cord-026306-mkmrninv 171 2 order order NN cord-026306-mkmrninv 171 3 to to TO cord-026306-mkmrninv 171 4 demonstrate demonstrate VB cord-026306-mkmrninv 171 5 the the DT cord-026306-mkmrninv 171 6 whole whole JJ cord-026306-mkmrninv 171 7 idea idea NN cord-026306-mkmrninv 171 8 let let VB cord-026306-mkmrninv 171 9 us -PRON- PRP cord-026306-mkmrninv 171 10 investigate investigate VB cord-026306-mkmrninv 171 11 the the DT cord-026306-mkmrninv 171 12 following follow VBG cord-026306-mkmrninv 171 13 example example NN cord-026306-mkmrninv 171 14 . . . cord-026306-mkmrninv 172 1 Assume assume VB cord-026306-mkmrninv 172 2 that that IN cord-026306-mkmrninv 172 3 the the DT cord-026306-mkmrninv 172 4 system system NN cord-026306-mkmrninv 172 5 of of IN cord-026306-mkmrninv 172 6 nodes node NNS cord-026306-mkmrninv 172 7 from from IN cord-026306-mkmrninv 172 8 the the DT cord-026306-mkmrninv 172 9 graph graph NN cord-026306-mkmrninv 172 10 on on IN cord-026306-mkmrninv 172 11 Fig Fig NNP cord-026306-mkmrninv 172 12 . . . cord-026306-mkmrninv 172 13 1 1 CD cord-026306-mkmrninv 172 14 also also RB cord-026306-mkmrninv 172 15 interacts interact VBZ cord-026306-mkmrninv 172 16 on on IN cord-026306-mkmrninv 172 17 another another DT cord-026306-mkmrninv 172 18 layer layer NN cord-026306-mkmrninv 172 19 as as IN cord-026306-mkmrninv 172 20 it -PRON- PRP cord-026306-mkmrninv 172 21 is be VBZ cord-026306-mkmrninv 172 22 shown show VBN cord-026306-mkmrninv 172 23 on on IN cord-026306-mkmrninv 172 24 Fig Fig NNP cord-026306-mkmrninv 172 25 . . . cord-026306-mkmrninv 173 1 2 2 LS cord-026306-mkmrninv 173 2 . . . cord-026306-mkmrninv 174 1 The the DT cord-026306-mkmrninv 174 2 sum sum NN cord-026306-mkmrninv 174 3 of of IN cord-026306-mkmrninv 174 4 weights weight NNS cord-026306-mkmrninv 174 5 for for IN cord-026306-mkmrninv 174 6 the the DT cord-026306-mkmrninv 174 7 second second JJ cord-026306-mkmrninv 174 8 graphs graphs NN cord-026306-mkmrninv 174 9 is be VBZ cord-026306-mkmrninv 174 10 |W |w CD cord-026306-mkmrninv 174 11 | | NN cord-026306-mkmrninv 174 12 = = SYM cord-026306-mkmrninv 174 13 4.2 4.2 CD cord-026306-mkmrninv 174 14 . . . cord-026306-mkmrninv 175 1 Hence hence RB cord-026306-mkmrninv 175 2 , , , cord-026306-mkmrninv 175 3 the the DT cord-026306-mkmrninv 175 4 belief belief NN cord-026306-mkmrninv 175 5 functions function NNS cord-026306-mkmrninv 175 6 for for IN cord-026306-mkmrninv 175 7 each each DT cord-026306-mkmrninv 175 8 node node NN cord-026306-mkmrninv 175 9 of of IN cord-026306-mkmrninv 175 10 the the DT cord-026306-mkmrninv 175 11 graph graph NN cord-026306-mkmrninv 175 12 on on IN cord-026306-mkmrninv 175 13 Fig Fig NNP cord-026306-mkmrninv 175 14 . . NNP cord-026306-mkmrninv 175 15 2 2 CD cord-026306-mkmrninv 175 16 with with IN cord-026306-mkmrninv 175 17 respect respect NN cord-026306-mkmrninv 175 18 to to IN cord-026306-mkmrninv 175 19 2-neighborhood 2-neighborhood CD cord-026306-mkmrninv 175 20 of of IN cord-026306-mkmrninv 175 21 nodes node NNS cord-026306-mkmrninv 175 22 are be VBP cord-026306-mkmrninv 175 23 following follow VBG cord-026306-mkmrninv 175 24 : : : cord-026306-mkmrninv 175 25 _SP cord-026306-mkmrninv 175 26 The the DT cord-026306-mkmrninv 175 27 matrix matrix NN cord-026306-mkmrninv 175 28 of of IN cord-026306-mkmrninv 175 29 pignistic pignistic JJ cord-026306-mkmrninv 175 30 probabilities probability NNS cord-026306-mkmrninv 175 31 Bet Bet NNP cord-026306-mkmrninv 175 32 As as IN cord-026306-mkmrninv 175 33 the the DT cord-026306-mkmrninv 175 34 result result NN cord-026306-mkmrninv 175 35 , , , cord-026306-mkmrninv 175 36 centrality centrality NN cord-026306-mkmrninv 175 37 vector vector NN cord-026306-mkmrninv 175 38 q q NNP cord-026306-mkmrninv 175 39 ( ( -LRB- cord-026306-mkmrninv 175 40 2 2 LS cord-026306-mkmrninv 175 41 ) ) -RRB- cord-026306-mkmrninv 175 42 is be VBZ cord-026306-mkmrninv 175 43 equal equal JJ cord-026306-mkmrninv 175 44 to to IN cord-026306-mkmrninv 175 45 ( ( -LRB- cord-026306-mkmrninv 175 46 1.261 1.261 CD cord-026306-mkmrninv 175 47 , , , cord-026306-mkmrninv 175 48 0.762 0.762 CD cord-026306-mkmrninv 175 49 , , , cord-026306-mkmrninv 175 50 0.928 0.928 CD cord-026306-mkmrninv 175 51 , , , cord-026306-mkmrninv 175 52 1.006 1.006 CD cord-026306-mkmrninv 175 53 , , , cord-026306-mkmrninv 175 54 1.045 1.045 CD cord-026306-mkmrninv 175 55 ) ) -RRB- cord-026306-mkmrninv 175 56 , , , cord-026306-mkmrninv 175 57 that that WDT cord-026306-mkmrninv 175 58 ranks rank VBZ cord-026306-mkmrninv 175 59 nodes node NNS cord-026306-mkmrninv 175 60 in in IN cord-026306-mkmrninv 175 61 the the DT cord-026306-mkmrninv 175 62 following following JJ cord-026306-mkmrninv 175 63 order order NN cord-026306-mkmrninv 175 64 : : : cord-026306-mkmrninv 175 65 v v NN cord-026306-mkmrninv 175 66 1 1 CD cord-026306-mkmrninv 175 67 v v NN cord-026306-mkmrninv 175 68 5 5 CD cord-026306-mkmrninv 175 69 v v NN cord-026306-mkmrninv 175 70 4 4 CD cord-026306-mkmrninv 175 71 v v NN cord-026306-mkmrninv 175 72 3 3 CD cord-026306-mkmrninv 175 73 v v NN cord-026306-mkmrninv 175 74 2 2 CD cord-026306-mkmrninv 175 75 , , , cord-026306-mkmrninv 175 76 that that WDT cord-026306-mkmrninv 175 77 also also RB cord-026306-mkmrninv 175 78 coincides coincide VBZ cord-026306-mkmrninv 175 79 with with IN cord-026306-mkmrninv 175 80 eigenvector eigenvector NN cord-026306-mkmrninv 175 81 centrality centrality NN cord-026306-mkmrninv 175 82 ranking ranking NN cord-026306-mkmrninv 175 83 . . . cord-026306-mkmrninv 176 1 We -PRON- PRP cord-026306-mkmrninv 176 2 now now RB cord-026306-mkmrninv 176 3 bring bring VBP cord-026306-mkmrninv 176 4 two two CD cord-026306-mkmrninv 176 5 graphs graph NNS cord-026306-mkmrninv 176 6 together together RB cord-026306-mkmrninv 176 7 and and CC cord-026306-mkmrninv 176 8 calculate calculate VB cord-026306-mkmrninv 176 9 pairwise pairwise JJ cord-026306-mkmrninv 176 10 aggregation aggregation NN cord-026306-mkmrninv 176 11 of of IN cord-026306-mkmrninv 176 12 belief belief NN cord-026306-mkmrninv 176 13 functions function NNS cord-026306-mkmrninv 177 1 g g NNP cord-026306-mkmrninv 177 2 ( ( -LRB- cord-026306-mkmrninv 177 3 1 1 CD cord-026306-mkmrninv 177 4 ) ) -RRB- cord-026306-mkmrninv 178 1 k k NNP cord-026306-mkmrninv 178 2 and and CC cord-026306-mkmrninv 178 3 g g NNP cord-026306-mkmrninv 179 1 ( ( -LRB- cord-026306-mkmrninv 179 2 2 2 LS cord-026306-mkmrninv 179 3 ) ) -RRB- cord-026306-mkmrninv 179 4 k k XX cord-026306-mkmrninv 179 5 with with IN cord-026306-mkmrninv 179 6 the the DT cord-026306-mkmrninv 179 7 help help NN cord-026306-mkmrninv 179 8 of of IN cord-026306-mkmrninv 179 9 Dempster Dempster NNP cord-026306-mkmrninv 179 10 rule rule NN cord-026306-mkmrninv 179 11 D D NNP cord-026306-mkmrninv 179 12 according accord VBG cord-026306-mkmrninv 179 13 to to IN cord-026306-mkmrninv 179 14 formula formula NN cord-026306-mkmrninv 179 15 ( ( -LRB- cord-026306-mkmrninv 179 16 1 1 CD cord-026306-mkmrninv 179 17 ) ) -RRB- cord-026306-mkmrninv 179 18 . . . cord-026306-mkmrninv 180 1 As as IN cord-026306-mkmrninv 180 2 the the DT cord-026306-mkmrninv 180 3 result result NN cord-026306-mkmrninv 180 4 , , , cord-026306-mkmrninv 180 5 we -PRON- PRP cord-026306-mkmrninv 180 6 obtain obtain VBP cord-026306-mkmrninv 180 7 new new JJ cord-026306-mkmrninv 180 8 belief belief NN cord-026306-mkmrninv 180 9 functions function NNS cord-026306-mkmrninv 180 10 g g NN cord-026306-mkmrninv 180 11 k k XX cord-026306-mkmrninv 181 1 = = NFP cord-026306-mkmrninv 181 2 D(g D(g NNP cord-026306-mkmrninv 182 1 ( ( -LRB- cord-026306-mkmrninv 182 2 1 1 CD cord-026306-mkmrninv 182 3 ) ) -RRB- cord-026306-mkmrninv 183 1 k k NNP cord-026306-mkmrninv 183 2 , , , cord-026306-mkmrninv 183 3 g g NNP cord-026306-mkmrninv 183 4 ( ( -LRB- cord-026306-mkmrninv 183 5 2 2 CD cord-026306-mkmrninv 183 6 ) ) -RRB- cord-026306-mkmrninv 183 7 k k NN cord-026306-mkmrninv 183 8 ) ) -RRB- cord-026306-mkmrninv 183 9 that that WDT cord-026306-mkmrninv 183 10 indicate indicate VBP cord-026306-mkmrninv 183 11 the the DT cord-026306-mkmrninv 183 12 interactions interaction NNS cord-026306-mkmrninv 183 13 between between IN cord-026306-mkmrninv 183 14 nodes node NNS cord-026306-mkmrninv 183 15 in in IN cord-026306-mkmrninv 183 16 the the DT cord-026306-mkmrninv 183 17 multiplex multiplex JJ cord-026306-mkmrninv 183 18 structure structure NN cord-026306-mkmrninv 183 19 . . . cord-026306-mkmrninv 184 1 Assuming assume VBG cord-026306-mkmrninv 184 2 that that IN cord-026306-mkmrninv 184 3 discounting discount VBG cord-026306-mkmrninv 184 4 parameter parameter NN cord-026306-mkmrninv 184 5 α α NN cord-026306-mkmrninv 184 6 = = SYM cord-026306-mkmrninv 184 7 0 0 CD cord-026306-mkmrninv 184 8 for for IN cord-026306-mkmrninv 184 9 both both DT cord-026306-mkmrninv 184 10 networks network NNS cord-026306-mkmrninv 184 11 we -PRON- PRP cord-026306-mkmrninv 184 12 obtain obtain VBP cord-026306-mkmrninv 184 13 the the DT cord-026306-mkmrninv 184 14 following follow VBG cord-026306-mkmrninv 184 15 belief belief NN cord-026306-mkmrninv 184 16 functions function NNS cord-026306-mkmrninv 184 17 : : : cord-026306-mkmrninv 184 18 Hence hence RB cord-026306-mkmrninv 184 19 , , , cord-026306-mkmrninv 184 20 the the DT cord-026306-mkmrninv 184 21 matrix matrix NN cord-026306-mkmrninv 184 22 of of IN cord-026306-mkmrninv 184 23 pignistic pignistic JJ cord-026306-mkmrninv 184 24 probabilities probability NNS cord-026306-mkmrninv 184 25 of of IN cord-026306-mkmrninv 184 26 aggregated aggregated JJ cord-026306-mkmrninv 184 27 belief belief NN cord-026306-mkmrninv 184 28 functions function NNS cord-026306-mkmrninv 184 29 is be VBZ cord-026306-mkmrninv 184 30 If if IN cord-026306-mkmrninv 184 31 we -PRON- PRP cord-026306-mkmrninv 184 32 average average VBP cord-026306-mkmrninv 184 33 over over IN cord-026306-mkmrninv 184 34 eigenvector eigenvector NN cord-026306-mkmrninv 184 35 centrality centrality NN cord-026306-mkmrninv 184 36 values value NNS cord-026306-mkmrninv 184 37 then then RB cord-026306-mkmrninv 184 38 we -PRON- PRP cord-026306-mkmrninv 184 39 obtain obtain VBP cord-026306-mkmrninv 184 40 the the DT cord-026306-mkmrninv 184 41 following following NN cord-026306-mkmrninv 184 42 , , , cord-026306-mkmrninv 184 43 that that IN cord-026306-mkmrninv 184 44 almost almost RB cord-026306-mkmrninv 184 45 agrees agree VBZ cord-026306-mkmrninv 184 46 with with IN cord-026306-mkmrninv 184 47 the the DT cord-026306-mkmrninv 184 48 ordering ordering NN cord-026306-mkmrninv 184 49 of of IN cord-026306-mkmrninv 184 50 the the DT cord-026306-mkmrninv 184 51 second second JJ cord-026306-mkmrninv 184 52 graph graph NN cord-026306-mkmrninv 184 53 . . . cord-026306-mkmrninv 185 1 As as IN cord-026306-mkmrninv 185 2 we -PRON- PRP cord-026306-mkmrninv 185 3 can can MD cord-026306-mkmrninv 185 4 see see VB cord-026306-mkmrninv 185 5 , , , cord-026306-mkmrninv 185 6 the the DT cord-026306-mkmrninv 185 7 results result NNS cord-026306-mkmrninv 185 8 obtained obtain VBN cord-026306-mkmrninv 185 9 by by IN cord-026306-mkmrninv 185 10 two two CD cord-026306-mkmrninv 185 11 approaches approach NNS cord-026306-mkmrninv 185 12 differ differ VBP cord-026306-mkmrninv 185 13 significantly significantly RB cord-026306-mkmrninv 185 14 . . . cord-026306-mkmrninv 186 1 This this DT cord-026306-mkmrninv 186 2 can can MD cord-026306-mkmrninv 186 3 be be VB cord-026306-mkmrninv 186 4 explained explain VBN cord-026306-mkmrninv 186 5 by by IN cord-026306-mkmrninv 186 6 the the DT cord-026306-mkmrninv 186 7 choice choice NN cord-026306-mkmrninv 186 8 of of IN cord-026306-mkmrninv 186 9 aggregation aggregation NN cord-026306-mkmrninv 186 10 rule rule NN cord-026306-mkmrninv 186 11 ( ( -LRB- cord-026306-mkmrninv 186 12 1 1 LS cord-026306-mkmrninv 186 13 ) ) -RRB- cord-026306-mkmrninv 186 14 that that WDT cord-026306-mkmrninv 186 15 takes take VBZ cord-026306-mkmrninv 186 16 into into IN cord-026306-mkmrninv 186 17 account account NN cord-026306-mkmrninv 186 18 the the DT cord-026306-mkmrninv 186 19 possible possible JJ cord-026306-mkmrninv 186 20 disagreement disagreement NN cord-026306-mkmrninv 186 21 in in IN cord-026306-mkmrninv 186 22 initial initial JJ cord-026306-mkmrninv 186 23 data datum NNS cord-026306-mkmrninv 186 24 . . . cord-026306-mkmrninv 187 1 It -PRON- PRP cord-026306-mkmrninv 187 2 means mean VBZ cord-026306-mkmrninv 187 3 that that IN cord-026306-mkmrninv 187 4 if if IN cord-026306-mkmrninv 187 5 the the DT cord-026306-mkmrninv 187 6 connections connection NNS cord-026306-mkmrninv 187 7 diverse diverse JJ cord-026306-mkmrninv 187 8 for for IN cord-026306-mkmrninv 187 9 some some DT cord-026306-mkmrninv 187 10 node node NN cord-026306-mkmrninv 187 11 on on IN cord-026306-mkmrninv 187 12 different different JJ cord-026306-mkmrninv 187 13 levels level NNS cord-026306-mkmrninv 187 14 of of IN cord-026306-mkmrninv 187 15 interaction interaction NN cord-026306-mkmrninv 187 16 it -PRON- PRP cord-026306-mkmrninv 187 17 leads lead VBZ cord-026306-mkmrninv 187 18 to to IN cord-026306-mkmrninv 187 19 the the DT cord-026306-mkmrninv 187 20 decrease decrease NN cord-026306-mkmrninv 187 21 of of IN cord-026306-mkmrninv 187 22 the the DT cord-026306-mkmrninv 187 23 importance importance NN cord-026306-mkmrninv 187 24 of of IN cord-026306-mkmrninv 187 25 this this DT cord-026306-mkmrninv 187 26 node node NN cord-026306-mkmrninv 187 27 in in IN cord-026306-mkmrninv 187 28 aggregated aggregate VBN cord-026306-mkmrninv 187 29 ranking ranking NN cord-026306-mkmrninv 187 30 . . . cord-026306-mkmrninv 188 1 This this DT cord-026306-mkmrninv 188 2 fact fact NN cord-026306-mkmrninv 188 3 can can MD cord-026306-mkmrninv 188 4 be be VB cord-026306-mkmrninv 188 5 seen see VBN cord-026306-mkmrninv 188 6 by by IN cord-026306-mkmrninv 188 7 the the DT cord-026306-mkmrninv 188 8 example example NN cord-026306-mkmrninv 188 9 of of IN cord-026306-mkmrninv 188 10 node node NN cord-026306-mkmrninv 188 11 1 1 CD cord-026306-mkmrninv 188 12 that that WDT cord-026306-mkmrninv 188 13 has have VBZ cord-026306-mkmrninv 188 14 only only RB cord-026306-mkmrninv 188 15 one one CD cord-026306-mkmrninv 188 16 strong strong JJ cord-026306-mkmrninv 188 17 connection connection NN cord-026306-mkmrninv 188 18 in in IN cord-026306-mkmrninv 188 19 the the DT cord-026306-mkmrninv 188 20 first first JJ cord-026306-mkmrninv 188 21 graph graph NN cord-026306-mkmrninv 188 22 and and CC cord-026306-mkmrninv 188 23 three three CD cord-026306-mkmrninv 188 24 connections connection NNS cord-026306-mkmrninv 188 25 in in IN cord-026306-mkmrninv 188 26 the the DT cord-026306-mkmrninv 188 27 second second JJ cord-026306-mkmrninv 188 28 graph graph NN cord-026306-mkmrninv 188 29 . . . cord-026306-mkmrninv 189 1 Despite despite IN cord-026306-mkmrninv 189 2 the the DT cord-026306-mkmrninv 189 3 fact fact NN cord-026306-mkmrninv 189 4 that that IN cord-026306-mkmrninv 189 5 this this DT cord-026306-mkmrninv 189 6 node node NN cord-026306-mkmrninv 189 7 is be VBZ cord-026306-mkmrninv 189 8 ranked rank VBN cord-026306-mkmrninv 189 9 as as IN cord-026306-mkmrninv 189 10 the the DT cord-026306-mkmrninv 189 11 first first JJ cord-026306-mkmrninv 189 12 for for IN cord-026306-mkmrninv 189 13 the the DT cord-026306-mkmrninv 189 14 second second JJ cord-026306-mkmrninv 189 15 network network NN cord-026306-mkmrninv 189 16 it -PRON- PRP cord-026306-mkmrninv 189 17 has have VBZ cord-026306-mkmrninv 189 18 low low JJ cord-026306-mkmrninv 189 19 position position NN cord-026306-mkmrninv 189 20 in in IN cord-026306-mkmrninv 189 21 aggregated aggregate VBN cord-026306-mkmrninv 189 22 ranking ranking NN cord-026306-mkmrninv 189 23 . . . cord-026306-mkmrninv 190 1 Another another DT cord-026306-mkmrninv 190 2 important important JJ cord-026306-mkmrninv 190 3 point point NN cord-026306-mkmrninv 190 4 is be VBZ cord-026306-mkmrninv 190 5 that that IN cord-026306-mkmrninv 190 6 stability stability NN cord-026306-mkmrninv 190 7 through through IN cord-026306-mkmrninv 190 8 all all DT cord-026306-mkmrninv 190 9 layers layer NNS cord-026306-mkmrninv 190 10 is be VBZ cord-026306-mkmrninv 190 11 encouraged encourage VBN cord-026306-mkmrninv 190 12 by by IN cord-026306-mkmrninv 190 13 higher high JJR cord-026306-mkmrninv 190 14 ranks rank NNS cord-026306-mkmrninv 190 15 . . . cord-026306-mkmrninv 191 1 For for IN cord-026306-mkmrninv 191 2 instance instance NN cord-026306-mkmrninv 191 3 , , , cord-026306-mkmrninv 191 4 node node NN cord-026306-mkmrninv 191 5 5 5 CD cord-026306-mkmrninv 191 6 is be VBZ cord-026306-mkmrninv 191 7 ranked rank VBN cord-026306-mkmrninv 191 8 as as IN cord-026306-mkmrninv 191 9 the the DT cord-026306-mkmrninv 191 10 first first JJ cord-026306-mkmrninv 191 11 one one CD cord-026306-mkmrninv 191 12 for for IN cord-026306-mkmrninv 191 13 both both DT cord-026306-mkmrninv 191 14 layers layer NNS cord-026306-mkmrninv 191 15 separately separately RB cord-026306-mkmrninv 191 16 . . . cord-026306-mkmrninv 192 1 However however RB cord-026306-mkmrninv 192 2 , , , cord-026306-mkmrninv 192 3 in in IN cord-026306-mkmrninv 192 4 aggregated aggregated JJ cord-026306-mkmrninv 192 5 ranking ranking NN cord-026306-mkmrninv 192 6 it -PRON- PRP cord-026306-mkmrninv 192 7 takes take VBZ cord-026306-mkmrninv 192 8 the the DT cord-026306-mkmrninv 192 9 first first JJ cord-026306-mkmrninv 192 10 place place NN cord-026306-mkmrninv 192 11 as as IN cord-026306-mkmrninv 192 12 this this DT cord-026306-mkmrninv 192 13 node node NN cord-026306-mkmrninv 192 14 demonstrates demonstrate VBZ cord-026306-mkmrninv 192 15 more more RBR cord-026306-mkmrninv 192 16 stable stable JJ cord-026306-mkmrninv 192 17 connections connection NNS cord-026306-mkmrninv 192 18 through through IN cord-026306-mkmrninv 192 19 both both DT cord-026306-mkmrninv 192 20 layers layer NNS cord-026306-mkmrninv 192 21 as as RB cord-026306-mkmrninv 192 22 well well RB cord-026306-mkmrninv 192 23 as as IN cord-026306-mkmrninv 192 24 node node NN cord-026306-mkmrninv 192 25 4 4 CD cord-026306-mkmrninv 192 26 . . . cord-026306-mkmrninv 193 1 Additionally additionally RB cord-026306-mkmrninv 193 2 , , , cord-026306-mkmrninv 193 3 if if IN cord-026306-mkmrninv 193 4 we -PRON- PRP cord-026306-mkmrninv 193 5 consider consider VBP cord-026306-mkmrninv 193 6 a a DT cord-026306-mkmrninv 193 7 1-neighborhood 1-neighborhood CD cord-026306-mkmrninv 193 8 of of IN cord-026306-mkmrninv 193 9 nodes node NNS cord-026306-mkmrninv 193 10 in in IN cord-026306-mkmrninv 193 11 multiplex multiplex JJ cord-026306-mkmrninv 193 12 acyclic acyclic JJ cord-026306-mkmrninv 193 13 graphs graph NNS cord-026306-mkmrninv 193 14 with with IN cord-026306-mkmrninv 193 15 two two CD cord-026306-mkmrninv 193 16 layers layer NNS cord-026306-mkmrninv 193 17 then then RB cord-026306-mkmrninv 193 18 the the DT cord-026306-mkmrninv 193 19 following follow VBG cord-026306-mkmrninv 193 20 propositions proposition NNS cord-026306-mkmrninv 193 21 concerning concern VBG cord-026306-mkmrninv 193 22 the the DT cord-026306-mkmrninv 193 23 aggregated aggregated JJ cord-026306-mkmrninv 193 24 interaction interaction NN cord-026306-mkmrninv 193 25 centrality centrality NN cord-026306-mkmrninv 193 26 value value NN cord-026306-mkmrninv 193 27 can can MD cord-026306-mkmrninv 193 28 be be VB cord-026306-mkmrninv 193 29 proved prove VBN cord-026306-mkmrninv 193 30 . . . cord-026306-mkmrninv 194 1 of of IN cord-026306-mkmrninv 194 2 node node NNP cord-026306-mkmrninv 194 3 v v NNP cord-026306-mkmrninv 194 4 and and CC cord-026306-mkmrninv 194 5 the the DT cord-026306-mkmrninv 194 6 Dempster Dempster NNP cord-026306-mkmrninv 194 7 combination combination NN cord-026306-mkmrninv 194 8 rule rule NN cord-026306-mkmrninv 194 9 ( ( -LRB- cord-026306-mkmrninv 194 10 1 1 CD cord-026306-mkmrninv 194 11 ) ) -RRB- cord-026306-mkmrninv 194 12 is be VBZ cord-026306-mkmrninv 194 13 used use VBN cord-026306-mkmrninv 194 14 then then RB cord-026306-mkmrninv 194 15 the the DT cord-026306-mkmrninv 194 16 aggregated aggregated JJ cord-026306-mkmrninv 194 17 interaction interaction NN cord-026306-mkmrninv 194 18 value value NN cord-026306-mkmrninv 194 19 of of IN cord-026306-mkmrninv 194 20 node node NN cord-026306-mkmrninv 194 21 v v NN cord-026306-mkmrninv 194 22 is be VBZ cord-026306-mkmrninv 194 23 equal equal JJ cord-026306-mkmrninv 194 24 to to IN cord-026306-mkmrninv 194 25 ( ( -LRB- cord-026306-mkmrninv 194 26 1 1 CD cord-026306-mkmrninv 194 27 ) ) -RRB- cord-026306-mkmrninv 194 28 , , , cord-026306-mkmrninv 194 29 e(u e(u NNP cord-026306-mkmrninv 194 30 , , , cord-026306-mkmrninv 194 31 y)∈E y)∈E NNP cord-026306-mkmrninv 195 1 ( ( -LRB- cord-026306-mkmrninv 195 2 2 2 LS cord-026306-mkmrninv 195 3 ) ) -RRB- cord-026306-mkmrninv 195 4 w w NN cord-026306-mkmrninv 195 5 ( ( -LRB- cord-026306-mkmrninv 195 6 1 1 CD cord-026306-mkmrninv 195 7 ) ) -RRB- cord-026306-mkmrninv 195 8 _SP cord-026306-mkmrninv 195 9 is be VBZ cord-026306-mkmrninv 195 10 the the DT cord-026306-mkmrninv 195 11 level level NN cord-026306-mkmrninv 195 12 of of IN cord-026306-mkmrninv 195 13 conflict conflict NN cord-026306-mkmrninv 195 14 of of IN cord-026306-mkmrninv 195 15 node node NN cord-026306-mkmrninv 195 16 u u NN cord-026306-mkmrninv 195 17 ∈ ∈ NN cord-026306-mkmrninv 195 18 V v NN cord-026306-mkmrninv 195 19 ; ; : cord-026306-mkmrninv 195 20 B(G B(G NNP cord-026306-mkmrninv 195 21 ) ) -RRB- cord-026306-mkmrninv 195 22 = = SYM cord-026306-mkmrninv 195 23 1 1 CD cord-026306-mkmrninv 195 24 n n NN cord-026306-mkmrninv 195 25 u∈V u∈V NNP cord-026306-mkmrninv 195 26 1 1 CD cord-026306-mkmrninv 195 27 is be VBZ cord-026306-mkmrninv 195 28 a a DT cord-026306-mkmrninv 195 29 constant constant JJ cord-026306-mkmrninv 195 30 that that WDT cord-026306-mkmrninv 195 31 is be VBZ cord-026306-mkmrninv 195 32 independent independent JJ cord-026306-mkmrninv 195 33 of of IN cord-026306-mkmrninv 195 34 node node NN cord-026306-mkmrninv 195 35 v. v. CC cord-026306-mkmrninv 195 36 If if IN cord-026306-mkmrninv 195 37 we -PRON- PRP cord-026306-mkmrninv 195 38 apply apply VBP cord-026306-mkmrninv 195 39 Yager Yager NNP cord-026306-mkmrninv 195 40 combination combination NN cord-026306-mkmrninv 195 41 rule rule NN cord-026306-mkmrninv 195 42 ( ( -LRB- cord-026306-mkmrninv 195 43 2 2 LS cord-026306-mkmrninv 195 44 ) ) -RRB- cord-026306-mkmrninv 195 45 then then RB cord-026306-mkmrninv 195 46 this this DT cord-026306-mkmrninv 195 47 expression expression NN cord-026306-mkmrninv 195 48 is be VBZ cord-026306-mkmrninv 195 49 simplified simplify VBN cord-026306-mkmrninv 195 50 . . . cord-026306-mkmrninv 196 1 Proposition proposition NN cord-026306-mkmrninv 196 2 3 3 CD cord-026306-mkmrninv 196 3 . . . cord-026306-mkmrninv 197 1 If if IN cord-026306-mkmrninv 197 2 centrality centrality NN cord-026306-mkmrninv 197 3 value value NN cord-026306-mkmrninv 197 4 q q NNP cord-026306-mkmrninv 197 5 v v NNP cord-026306-mkmrninv 197 6 for for IN cord-026306-mkmrninv 197 7 node node NN cord-026306-mkmrninv 197 8 v v NNP cord-026306-mkmrninv 197 9 ∈ ∈ NN cord-026306-mkmrninv 197 10 V v NN cord-026306-mkmrninv 197 11 in in IN cord-026306-mkmrninv 197 12 acyclic acyclic JJ cord-026306-mkmrninv 197 13 graph graph NN cord-026306-mkmrninv 197 14 G g NN cord-026306-mkmrninv 197 15 = = NFP cord-026306-mkmrninv 198 1 ( ( -LRB- cord-026306-mkmrninv 198 2 V v NN cord-026306-mkmrninv 198 3 , , , cord-026306-mkmrninv 198 4 E E NNP cord-026306-mkmrninv 198 5 ( ( -LRB- cord-026306-mkmrninv 198 6 s s NNP cord-026306-mkmrninv 198 7 ) ) -RRB- cord-026306-mkmrninv 198 8 , , , cord-026306-mkmrninv 198 9 W W NNP cord-026306-mkmrninv 198 10 ( ( -LRB- cord-026306-mkmrninv 198 11 s s NN cord-026306-mkmrninv 198 12 ) ) -RRB- cord-026306-mkmrninv 198 13 ) ) -RRB- cord-026306-mkmrninv 198 14 , , , cord-026306-mkmrninv 198 15 s s NN cord-026306-mkmrninv 198 16 = = SYM cord-026306-mkmrninv 198 17 1 1 CD cord-026306-mkmrninv 198 18 , , , cord-026306-mkmrninv 198 19 2 2 CD cord-026306-mkmrninv 198 20 , , , cord-026306-mkmrninv 198 21 |V |v CD cord-026306-mkmrninv 198 22 | | NNP cord-026306-mkmrninv 198 23 = = SYM cord-026306-mkmrninv 198 24 n n NNP cord-026306-mkmrninv 198 25 , , , cord-026306-mkmrninv 198 26 n n NN cord-026306-mkmrninv 198 27 ≥ ≥ CD cord-026306-mkmrninv 198 28 2 2 CD cord-026306-mkmrninv 198 29 is be VBZ cord-026306-mkmrninv 198 30 calculated calculate VBN cord-026306-mkmrninv 198 31 with with IN cord-026306-mkmrninv 198 32 regard regard NN cord-026306-mkmrninv 198 33 to to IN cord-026306-mkmrninv 198 34 1neighborhood 1neighborhood CD cord-026306-mkmrninv 198 35 N n CD cord-026306-mkmrninv 198 36 ( ( -LRB- cord-026306-mkmrninv 198 37 1 1 CD cord-026306-mkmrninv 198 38 ) ) -RRB- cord-026306-mkmrninv 198 39 v v NN cord-026306-mkmrninv 198 40 of of IN cord-026306-mkmrninv 198 41 node node NN cord-026306-mkmrninv 198 42 v v NN cord-026306-mkmrninv 198 43 and and CC cord-026306-mkmrninv 198 44 the the DT cord-026306-mkmrninv 198 45 Yager Yager NNP cord-026306-mkmrninv 198 46 combination combination NN cord-026306-mkmrninv 198 47 rule rule NN cord-026306-mkmrninv 198 48 ( ( -LRB- cord-026306-mkmrninv 198 49 2 2 CD cord-026306-mkmrninv 198 50 ) ) -RRB- cord-026306-mkmrninv 198 51 is be VBZ cord-026306-mkmrninv 198 52 used use VBN cord-026306-mkmrninv 198 53 then then RB cord-026306-mkmrninv 198 54 the the DT cord-026306-mkmrninv 198 55 aggregated aggregated JJ cord-026306-mkmrninv 198 56 interaction interaction NN cord-026306-mkmrninv 198 57 value value NN cord-026306-mkmrninv 198 58 of of IN cord-026306-mkmrninv 198 59 node node NN cord-026306-mkmrninv 198 60 v v NN cord-026306-mkmrninv 198 61 is be VBZ cord-026306-mkmrninv 198 62 equal equal JJ cord-026306-mkmrninv 198 63 to to IN cord-026306-mkmrninv 198 64 is be VBZ cord-026306-mkmrninv 198 65 a a DT cord-026306-mkmrninv 198 66 constant constant JJ cord-026306-mkmrninv 198 67 that that WDT cord-026306-mkmrninv 198 68 is be VBZ cord-026306-mkmrninv 198 69 independent independent JJ cord-026306-mkmrninv 198 70 of of IN cord-026306-mkmrninv 198 71 node node NN cord-026306-mkmrninv 198 72 v. v. NNP cord-026306-mkmrninv 199 1 It -PRON- PRP cord-026306-mkmrninv 199 2 can can MD cord-026306-mkmrninv 199 3 be be VB cord-026306-mkmrninv 199 4 seen see VBN cord-026306-mkmrninv 199 5 that that IN cord-026306-mkmrninv 199 6 in in IN cord-026306-mkmrninv 199 7 the the DT cord-026306-mkmrninv 199 8 last last JJ cord-026306-mkmrninv 199 9 case case NN cord-026306-mkmrninv 199 10 the the DT cord-026306-mkmrninv 199 11 aggregated aggregated JJ cord-026306-mkmrninv 199 12 interaction interaction NN cord-026306-mkmrninv 199 13 centrality centrality NN cord-026306-mkmrninv 199 14 value value NN cord-026306-mkmrninv 199 15 of of IN cord-026306-mkmrninv 199 16 node node NN cord-026306-mkmrninv 199 17 v v NN cord-026306-mkmrninv 199 18 is be VBZ cord-026306-mkmrninv 199 19 represented represent VBN cord-026306-mkmrninv 199 20 as as IN cord-026306-mkmrninv 199 21 a a DT cord-026306-mkmrninv 199 22 sum sum NN cord-026306-mkmrninv 199 23 of of IN cord-026306-mkmrninv 199 24 normalized normalized JJ cord-026306-mkmrninv 199 25 weighted weighted JJ cord-026306-mkmrninv 199 26 degree degree NN cord-026306-mkmrninv 199 27 centralities centrality NNS cord-026306-mkmrninv 199 28 on on IN cord-026306-mkmrninv 199 29 each each DT cord-026306-mkmrninv 199 30 layer layer NN cord-026306-mkmrninv 199 31 and and CC cord-026306-mkmrninv 199 32 the the DT cord-026306-mkmrninv 199 33 value value NN cord-026306-mkmrninv 199 34 that that WDT cord-026306-mkmrninv 199 35 represents represent VBZ cord-026306-mkmrninv 199 36 the the DT cord-026306-mkmrninv 199 37 interactions interaction NNS cord-026306-mkmrninv 199 38 of of IN cord-026306-mkmrninv 199 39 v v NN cord-026306-mkmrninv 199 40 's 's POS cord-026306-mkmrninv 199 41 neighbors neighbor NNS cord-026306-mkmrninv 199 42 through through IN cord-026306-mkmrninv 199 43 different different JJ cord-026306-mkmrninv 199 44 layers layer NNS cord-026306-mkmrninv 199 45 . . . cord-026306-mkmrninv 200 1 In in IN cord-026306-mkmrninv 200 2 this this DT cord-026306-mkmrninv 200 3 work work NN cord-026306-mkmrninv 200 4 we -PRON- PRP cord-026306-mkmrninv 200 5 propose propose VBP cord-026306-mkmrninv 200 6 a a DT cord-026306-mkmrninv 200 7 new new JJ cord-026306-mkmrninv 200 8 approach approach NN cord-026306-mkmrninv 200 9 for for IN cord-026306-mkmrninv 200 10 the the DT cord-026306-mkmrninv 200 11 nodes node NNS cord-026306-mkmrninv 200 12 importance importance NN cord-026306-mkmrninv 200 13 assessment assessment NN cord-026306-mkmrninv 200 14 in in IN cord-026306-mkmrninv 200 15 multiplex multiplex NN cord-026306-mkmrninv 200 16 networks network NNS cord-026306-mkmrninv 200 17 . . . cord-026306-mkmrninv 201 1 We -PRON- PRP cord-026306-mkmrninv 201 2 apply apply VBP cord-026306-mkmrninv 201 3 Dempster Dempster NNP cord-026306-mkmrninv 201 4 - - HYPH cord-026306-mkmrninv 201 5 Shafer Shafer NNP cord-026306-mkmrninv 201 6 theory theory NN cord-026306-mkmrninv 201 7 in in IN cord-026306-mkmrninv 201 8 order order NN cord-026306-mkmrninv 201 9 to to TO cord-026306-mkmrninv 201 10 reveal reveal VB cord-026306-mkmrninv 201 11 key key JJ cord-026306-mkmrninv 201 12 elements element NNS cord-026306-mkmrninv 201 13 in in IN cord-026306-mkmrninv 201 14 undirected undirected JJ cord-026306-mkmrninv 201 15 weighted weighted JJ cord-026306-mkmrninv 201 16 graphs graph NNS cord-026306-mkmrninv 201 17 as as RB cord-026306-mkmrninv 201 18 well well RB cord-026306-mkmrninv 201 19 as as IN cord-026306-mkmrninv 201 20 to to TO cord-026306-mkmrninv 201 21 aggregate aggregate VB cord-026306-mkmrninv 201 22 interactions interaction NNS cord-026306-mkmrninv 201 23 between between IN cord-026306-mkmrninv 201 24 nodes node NNS cord-026306-mkmrninv 201 25 into into IN cord-026306-mkmrninv 201 26 the the DT cord-026306-mkmrninv 201 27 total total JJ cord-026306-mkmrninv 201 28 ranking ranking NN cord-026306-mkmrninv 201 29 . . . cord-026306-mkmrninv 202 1 We -PRON- PRP cord-026306-mkmrninv 202 2 assess assess VBP cord-026306-mkmrninv 202 3 the the DT cord-026306-mkmrninv 202 4 cooperation cooperation NN cord-026306-mkmrninv 202 5 of of IN cord-026306-mkmrninv 202 6 nodes node NNS cord-026306-mkmrninv 202 7 with with IN cord-026306-mkmrninv 202 8 different different JJ cord-026306-mkmrninv 202 9 subgroups subgroup NNS cord-026306-mkmrninv 202 10 of of IN cord-026306-mkmrninv 202 11 vertices vertex NNS cord-026306-mkmrninv 202 12 by by IN cord-026306-mkmrninv 202 13 evaluating evaluate VBG cord-026306-mkmrninv 202 14 the the DT cord-026306-mkmrninv 202 15 corresponding corresponding JJ cord-026306-mkmrninv 202 16 belief belief NN cord-026306-mkmrninv 202 17 functions function NNS cord-026306-mkmrninv 202 18 . . . cord-026306-mkmrninv 203 1 The the DT cord-026306-mkmrninv 203 2 proposed propose VBN cord-026306-mkmrninv 203 3 model model NN cord-026306-mkmrninv 203 4 of of IN cord-026306-mkmrninv 203 5 belief belief NN cord-026306-mkmrninv 203 6 function function NN cord-026306-mkmrninv 203 7 takes take VBZ cord-026306-mkmrninv 203 8 into into IN cord-026306-mkmrninv 203 9 account account NN cord-026306-mkmrninv 203 10 the the DT cord-026306-mkmrninv 203 11 cooperation cooperation NN cord-026306-mkmrninv 203 12 with with IN cord-026306-mkmrninv 203 13 nodes node NNS cord-026306-mkmrninv 203 14 and and CC cord-026306-mkmrninv 203 15 the the DT cord-026306-mkmrninv 203 16 groups group NNS cord-026306-mkmrninv 203 17 of of IN cord-026306-mkmrninv 203 18 nodes node NNS cord-026306-mkmrninv 203 19 that that WDT cord-026306-mkmrninv 203 20 are be VBP cord-026306-mkmrninv 203 21 located locate VBN cord-026306-mkmrninv 203 22 in in IN cord-026306-mkmrninv 203 23 a a DT cord-026306-mkmrninv 203 24 given give VBN cord-026306-mkmrninv 203 25 neighborhood neighborhood NN cord-026306-mkmrninv 203 26 of of IN cord-026306-mkmrninv 203 27 a a DT cord-026306-mkmrninv 203 28 considered consider VBN cord-026306-mkmrninv 203 29 vertex vertex NN cord-026306-mkmrninv 203 30 . . . cord-026306-mkmrninv 204 1 Further further RB cord-026306-mkmrninv 204 2 , , , cord-026306-mkmrninv 204 3 the the DT cord-026306-mkmrninv 204 4 obtained obtain VBN cord-026306-mkmrninv 204 5 intensities intensity NNS cord-026306-mkmrninv 204 6 of of IN cord-026306-mkmrninv 204 7 cooperation cooperation NN cord-026306-mkmrninv 204 8 with with IN cord-026306-mkmrninv 204 9 different different JJ cord-026306-mkmrninv 204 10 groups group NNS cord-026306-mkmrninv 204 11 of of IN cord-026306-mkmrninv 204 12 nodes node NNS cord-026306-mkmrninv 204 13 are be VBP cord-026306-mkmrninv 204 14 redistributed redistribute VBN cord-026306-mkmrninv 204 15 among among IN cord-026306-mkmrninv 204 16 the the DT cord-026306-mkmrninv 204 17 participants participant NNS cord-026306-mkmrninv 204 18 of of IN cord-026306-mkmrninv 204 19 these these DT cord-026306-mkmrninv 204 20 groups group NNS cord-026306-mkmrninv 204 21 that that WDT cord-026306-mkmrninv 204 22 results result VBZ cord-026306-mkmrninv 204 23 in in IN cord-026306-mkmrninv 204 24 node node NN cord-026306-mkmrninv 204 25 - - HYPH cord-026306-mkmrninv 204 26 to to IN cord-026306-mkmrninv 204 27 - - HYPH cord-026306-mkmrninv 204 28 node node NN cord-026306-mkmrninv 204 29 intensity intensity NN cord-026306-mkmrninv 204 30 of of IN cord-026306-mkmrninv 204 31 cooperation cooperation NN cord-026306-mkmrninv 204 32 . . . cord-026306-mkmrninv 205 1 The the DT cord-026306-mkmrninv 205 2 obtained obtain VBN cord-026306-mkmrninv 205 3 values value NNS cord-026306-mkmrninv 205 4 show show VBP cord-026306-mkmrninv 205 5 real real JJ cord-026306-mkmrninv 205 6 interactions interaction NNS cord-026306-mkmrninv 205 7 between between IN cord-026306-mkmrninv 205 8 nodes node NNS cord-026306-mkmrninv 205 9 with with IN cord-026306-mkmrninv 205 10 respect respect NN cord-026306-mkmrninv 205 11 to to IN cord-026306-mkmrninv 205 12 distant distant JJ cord-026306-mkmrninv 205 13 connections connection NNS cord-026306-mkmrninv 205 14 , , , cord-026306-mkmrninv 205 15 that that WDT cord-026306-mkmrninv 205 16 is be VBZ cord-026306-mkmrninv 205 17 already already RB cord-026306-mkmrninv 205 18 informative informative JJ cord-026306-mkmrninv 205 19 and and CC cord-026306-mkmrninv 205 20 can can MD cord-026306-mkmrninv 205 21 not not RB cord-026306-mkmrninv 205 22 be be VB cord-026306-mkmrninv 205 23 derived derive VBN cord-026306-mkmrninv 205 24 with with IN cord-026306-mkmrninv 205 25 most most JJS cord-026306-mkmrninv 205 26 of of IN cord-026306-mkmrninv 205 27 the the DT cord-026306-mkmrninv 205 28 classical classical JJ cord-026306-mkmrninv 205 29 centrality centrality NN cord-026306-mkmrninv 205 30 measures measure NNS cord-026306-mkmrninv 205 31 . . . cord-026306-mkmrninv 206 1 Finally finally RB cord-026306-mkmrninv 206 2 , , , cord-026306-mkmrninv 206 3 we -PRON- PRP cord-026306-mkmrninv 206 4 aggregate aggregate VBP cord-026306-mkmrninv 206 5 the the DT cord-026306-mkmrninv 206 6 pairwise pairwise JJ cord-026306-mkmrninv 206 7 interaction interaction NN cord-026306-mkmrninv 206 8 into into IN cord-026306-mkmrninv 206 9 the the DT cord-026306-mkmrninv 206 10 final final JJ cord-026306-mkmrninv 206 11 centrality centrality NN cord-026306-mkmrninv 206 12 vector vector NN cord-026306-mkmrninv 206 13 that that WDT cord-026306-mkmrninv 206 14 gives give VBZ cord-026306-mkmrninv 206 15 the the DT cord-026306-mkmrninv 206 16 ranking ranking NN cord-026306-mkmrninv 206 17 of of IN cord-026306-mkmrninv 206 18 nodes node NNS cord-026306-mkmrninv 206 19 and and CC cord-026306-mkmrninv 206 20 helps help VBZ cord-026306-mkmrninv 206 21 to to TO cord-026306-mkmrninv 206 22 reveal reveal VB cord-026306-mkmrninv 206 23 key key JJ cord-026306-mkmrninv 206 24 elements element NNS cord-026306-mkmrninv 206 25 in in IN cord-026306-mkmrninv 206 26 a a DT cord-026306-mkmrninv 206 27 network network NN cord-026306-mkmrninv 206 28 . . . cord-026306-mkmrninv 207 1 If if IN cord-026306-mkmrninv 207 2 nodes node NNS cord-026306-mkmrninv 207 3 cooperate cooperate VBP cord-026306-mkmrninv 207 4 with with IN cord-026306-mkmrninv 207 5 each each DT cord-026306-mkmrninv 207 6 other other JJ cord-026306-mkmrninv 207 7 on on IN cord-026306-mkmrninv 207 8 different different JJ cord-026306-mkmrninv 207 9 levels level NNS cord-026306-mkmrninv 207 10 of of IN cord-026306-mkmrninv 207 11 interactions interaction NNS cord-026306-mkmrninv 207 12 then then RB cord-026306-mkmrninv 207 13 we -PRON- PRP cord-026306-mkmrninv 207 14 apply apply VBP cord-026306-mkmrninv 207 15 a a DT cord-026306-mkmrninv 207 16 combination combination NN cord-026306-mkmrninv 207 17 rule rule NN cord-026306-mkmrninv 207 18 to to IN cord-026306-mkmrninv 207 19 mass mass NN cord-026306-mkmrninv 207 20 functions function NNS cord-026306-mkmrninv 207 21 obtained obtain VBN cord-026306-mkmrninv 207 22 for for IN cord-026306-mkmrninv 207 23 different different JJ cord-026306-mkmrninv 207 24 layers layer NNS cord-026306-mkmrninv 207 25 of of IN cord-026306-mkmrninv 207 26 a a DT cord-026306-mkmrninv 207 27 multiplex multiplex JJ cord-026306-mkmrninv 207 28 structure structure NN cord-026306-mkmrninv 207 29 . . . cord-026306-mkmrninv 208 1 In in IN cord-026306-mkmrninv 208 2 particular particular JJ cord-026306-mkmrninv 208 3 , , , cord-026306-mkmrninv 208 4 Dempster Dempster NNP cord-026306-mkmrninv 208 5 rule rule NN cord-026306-mkmrninv 208 6 takes take VBZ cord-026306-mkmrninv 208 7 into into IN cord-026306-mkmrninv 208 8 account account NN cord-026306-mkmrninv 208 9 the the DT cord-026306-mkmrninv 208 10 disagreement disagreement NN cord-026306-mkmrninv 208 11 in in IN cord-026306-mkmrninv 208 12 data datum NNS cord-026306-mkmrninv 208 13 on on IN cord-026306-mkmrninv 208 14 different different JJ cord-026306-mkmrninv 208 15 levels level NNS cord-026306-mkmrninv 208 16 of of IN cord-026306-mkmrninv 208 17 interaction interaction NN cord-026306-mkmrninv 208 18 , , , cord-026306-mkmrninv 208 19 i.e. i.e. FW cord-026306-mkmrninv 208 20 it -PRON- PRP cord-026306-mkmrninv 208 21 rewards reward VBZ cord-026306-mkmrninv 208 22 nodes node NNS cord-026306-mkmrninv 208 23 that that WDT cord-026306-mkmrninv 208 24 have have VBP cord-026306-mkmrninv 208 25 consistent consistent JJ cord-026306-mkmrninv 208 26 connections connection NNS cord-026306-mkmrninv 208 27 through through IN cord-026306-mkmrninv 208 28 all all DT cord-026306-mkmrninv 208 29 layers layer NNS cord-026306-mkmrninv 208 30 and and CC cord-026306-mkmrninv 208 31 reduces reduce VBZ cord-026306-mkmrninv 208 32 the the DT cord-026306-mkmrninv 208 33 importance importance NN cord-026306-mkmrninv 208 34 of of IN cord-026306-mkmrninv 208 35 nodes node NNS cord-026306-mkmrninv 208 36 with with IN cord-026306-mkmrninv 208 37 unstable unstable JJ cord-026306-mkmrninv 208 38 links link NNS cord-026306-mkmrninv 208 39 . . . cord-026306-mkmrninv 209 1 Additionally additionally RB cord-026306-mkmrninv 209 2 , , , cord-026306-mkmrninv 209 3 other other JJ cord-026306-mkmrninv 209 4 combination combination NN cord-026306-mkmrninv 209 5 rules rule NNS cord-026306-mkmrninv 209 6 can can MD cord-026306-mkmrninv 209 7 be be VB cord-026306-mkmrninv 209 8 used use VBN cord-026306-mkmrninv 209 9 as as RB cord-026306-mkmrninv 209 10 well well RB cord-026306-mkmrninv 209 11 in in IN cord-026306-mkmrninv 209 12 order order NN cord-026306-mkmrninv 209 13 to to TO cord-026306-mkmrninv 209 14 estimate estimate VB cord-026306-mkmrninv 209 15 the the DT cord-026306-mkmrninv 209 16 aggregated aggregated JJ cord-026306-mkmrninv 209 17 centralities centrality NNS cord-026306-mkmrninv 209 18 in in IN cord-026306-mkmrninv 209 19 multilayer multilayer JJ cord-026306-mkmrninv 209 20 networks network NNS cord-026306-mkmrninv 209 21 . . . cord-026306-mkmrninv 210 1 These these DT cord-026306-mkmrninv 210 2 rules rule NNS cord-026306-mkmrninv 210 3 may may MD cord-026306-mkmrninv 210 4 consider consider VB cord-026306-mkmrninv 210 5 the the DT cord-026306-mkmrninv 210 6 reliability reliability NN cord-026306-mkmrninv 210 7 , , , cord-026306-mkmrninv 210 8 the the DT cord-026306-mkmrninv 210 9 inconsistency inconsistency NN cord-026306-mkmrninv 210 10 , , , cord-026306-mkmrninv 210 11 the the DT cord-026306-mkmrninv 210 12 uncertainty uncertainty NN cord-026306-mkmrninv 210 13 , , , cord-026306-mkmrninv 210 14 etc etc FW cord-026306-mkmrninv 210 15 . . . cord-026306-mkmrninv 211 1 of of IN cord-026306-mkmrninv 211 2 a a DT cord-026306-mkmrninv 211 3 network network NN cord-026306-mkmrninv 211 4 structure structure NN cord-026306-mkmrninv 211 5 in in IN cord-026306-mkmrninv 211 6 various various JJ cord-026306-mkmrninv 211 7 ways way NNS cord-026306-mkmrninv 211 8 . . . cord-026306-mkmrninv 212 1 It -PRON- PRP cord-026306-mkmrninv 212 2 is be VBZ cord-026306-mkmrninv 212 3 important important JJ cord-026306-mkmrninv 212 4 to to TO cord-026306-mkmrninv 212 5 note note VB cord-026306-mkmrninv 212 6 that that IN cord-026306-mkmrninv 212 7 the the DT cord-026306-mkmrninv 212 8 proposed propose VBN cord-026306-mkmrninv 212 9 approach approach NN cord-026306-mkmrninv 212 10 can can MD cord-026306-mkmrninv 212 11 be be VB cord-026306-mkmrninv 212 12 easily easily RB cord-026306-mkmrninv 212 13 adapted adapt VBN cord-026306-mkmrninv 212 14 to to IN cord-026306-mkmrninv 212 15 directed direct VBN cord-026306-mkmrninv 212 16 networks network NNS cord-026306-mkmrninv 212 17 . . . cord-026306-mkmrninv 213 1 We -PRON- PRP cord-026306-mkmrninv 213 2 also also RB cord-026306-mkmrninv 213 3 emphasize emphasize VBP cord-026306-mkmrninv 213 4 that that IN cord-026306-mkmrninv 213 5 parameters parameter NNS cord-026306-mkmrninv 213 6 of of IN cord-026306-mkmrninv 213 7 the the DT cord-026306-mkmrninv 213 8 introduced introduce VBN cord-026306-mkmrninv 213 9 functions function NNS cord-026306-mkmrninv 213 10 such such JJ cord-026306-mkmrninv 213 11 as as IN cord-026306-mkmrninv 213 12 discounting discount VBG cord-026306-mkmrninv 213 13 coefficients coefficient NNS cord-026306-mkmrninv 213 14 , , , cord-026306-mkmrninv 213 15 the the DT cord-026306-mkmrninv 213 16 radius radius NN cord-026306-mkmrninv 213 17 of of IN cord-026306-mkmrninv 213 18 nodes node NNS cord-026306-mkmrninv 213 19 neighborhood neighborhood NN cord-026306-mkmrninv 213 20 , , , cord-026306-mkmrninv 213 21 etc etc FW cord-026306-mkmrninv 213 22 . . . cord-026306-mkmrninv 213 23 can can MD cord-026306-mkmrninv 213 24 be be VB cord-026306-mkmrninv 213 25 tuned tune VBN cord-026306-mkmrninv 213 26 in in IN cord-026306-mkmrninv 213 27 accordance accordance NN cord-026306-mkmrninv 213 28 with with IN cord-026306-mkmrninv 213 29 the the DT cord-026306-mkmrninv 213 30 problem problem NN cord-026306-mkmrninv 213 31 statement statement NN cord-026306-mkmrninv 213 32 . . . cord-026306-mkmrninv 214 1 It -PRON- PRP cord-026306-mkmrninv 214 2 is be VBZ cord-026306-mkmrninv 214 3 also also RB cord-026306-mkmrninv 214 4 shown show VBN cord-026306-mkmrninv 214 5 that that IN cord-026306-mkmrninv 214 6 the the DT cord-026306-mkmrninv 214 7 proposed propose VBN cord-026306-mkmrninv 214 8 methods method NNS cord-026306-mkmrninv 214 9 give give VBP cord-026306-mkmrninv 214 10 comparable comparable JJ cord-026306-mkmrninv 214 11 results result NNS cord-026306-mkmrninv 214 12 for for IN cord-026306-mkmrninv 214 13 onelayer onelayer NN cord-026306-mkmrninv 214 14 networks network NNS cord-026306-mkmrninv 214 15 and and CC cord-026306-mkmrninv 214 16 take take VB cord-026306-mkmrninv 214 17 into into IN cord-026306-mkmrninv 214 18 account account NN cord-026306-mkmrninv 214 19 specifications specification NNS cord-026306-mkmrninv 214 20 of of IN cord-026306-mkmrninv 214 21 a a DT cord-026306-mkmrninv 214 22 multilayer multilayer JJ cord-026306-mkmrninv 214 23 structure structure NN cord-026306-mkmrninv 214 24 . . . cord-026306-mkmrninv 215 1 In in IN cord-026306-mkmrninv 215 2 further further JJ cord-026306-mkmrninv 215 3 research research NN cord-026306-mkmrninv 215 4 we -PRON- PRP cord-026306-mkmrninv 215 5 aim aim VBP cord-026306-mkmrninv 215 6 to to TO cord-026306-mkmrninv 215 7 improve improve VB cord-026306-mkmrninv 215 8 the the DT cord-026306-mkmrninv 215 9 proposed propose VBN cord-026306-mkmrninv 215 10 approach approach NN cord-026306-mkmrninv 215 11 and and CC cord-026306-mkmrninv 215 12 apply apply VB cord-026306-mkmrninv 215 13 the the DT cord-026306-mkmrninv 215 14 developed develop VBN cord-026306-mkmrninv 215 15 methods method NNS cord-026306-mkmrninv 215 16 to to IN cord-026306-mkmrninv 215 17 real real JJ cord-026306-mkmrninv 215 18 networks network NNS cord-026306-mkmrninv 215 19 . . . cord-026306-mkmrninv 216 1 Upper upper JJ cord-026306-mkmrninv 216 2 and and CC cord-026306-mkmrninv 216 3 lower low JJR cord-026306-mkmrninv 216 4 probabilities probability NNS cord-026306-mkmrninv 216 5 induced induce VBN cord-026306-mkmrninv 216 6 by by IN cord-026306-mkmrninv 216 7 a a DT cord-026306-mkmrninv 216 8 multivalued multivalued JJ cord-026306-mkmrninv 216 9 mapping mapping NN cord-026306-mkmrninv 216 10 Mathematical Mathematical NNP cord-026306-mkmrninv 216 11 Theory Theory NNP cord-026306-mkmrninv 216 12 of of IN cord-026306-mkmrninv 216 13 Evidence Evidence NNP cord-026306-mkmrninv 216 14 Belief Belief NNP cord-026306-mkmrninv 216 15 approach approach NN cord-026306-mkmrninv 216 16 for for IN cord-026306-mkmrninv 216 17 social social JJ cord-026306-mkmrninv 216 18 networks network NNS cord-026306-mkmrninv 216 19 A a DT cord-026306-mkmrninv 216 20 modified modify VBN cord-026306-mkmrninv 216 21 evidential evidential JJ cord-026306-mkmrninv 216 22 methodology methodology NN cord-026306-mkmrninv 216 23 of of IN cord-026306-mkmrninv 216 24 identifying identify VBG cord-026306-mkmrninv 216 25 influential influential JJ cord-026306-mkmrninv 216 26 nodes node NNS cord-026306-mkmrninv 216 27 in in IN cord-026306-mkmrninv 216 28 weighted weighted JJ cord-026306-mkmrninv 216 29 networks network NNS cord-026306-mkmrninv 217 1 A a DT cord-026306-mkmrninv 217 2 reliability reliability NN cord-026306-mkmrninv 217 3 - - HYPH cord-026306-mkmrninv 217 4 based base VBN cord-026306-mkmrninv 217 5 approach approach NN cord-026306-mkmrninv 217 6 for for IN cord-026306-mkmrninv 217 7 influence influence NN cord-026306-mkmrninv 217 8 maximization maximization NN cord-026306-mkmrninv 217 9 using use VBG cord-026306-mkmrninv 217 10 the the DT cord-026306-mkmrninv 217 11 evidence evidence NN cord-026306-mkmrninv 217 12 theory theory NN cord-026306-mkmrninv 217 13 Evidential evidential JJ cord-026306-mkmrninv 217 14 community community NN cord-026306-mkmrninv 217 15 detection detection NN cord-026306-mkmrninv 217 16 based base VBN cord-026306-mkmrninv 217 17 on on IN cord-026306-mkmrninv 217 18 density density NN cord-026306-mkmrninv 217 19 peaks peak NNS cord-026306-mkmrninv 217 20 Networks network NNS cord-026306-mkmrninv 217 21 : : : cord-026306-mkmrninv 217 22 An an DT cord-026306-mkmrninv 217 23 Introduction Introduction NNP cord-026306-mkmrninv 217 24 Power power NN cord-026306-mkmrninv 217 25 and and CC cord-026306-mkmrninv 217 26 centrality centrality NN cord-026306-mkmrninv 217 27 : : : cord-026306-mkmrninv 217 28 a a DT cord-026306-mkmrninv 217 29 family family NN cord-026306-mkmrninv 217 30 of of IN cord-026306-mkmrninv 217 31 measures measure NNS cord-026306-mkmrninv 217 32 The the DT cord-026306-mkmrninv 217 33 anatomy anatomy NN cord-026306-mkmrninv 217 34 of of IN cord-026306-mkmrninv 217 35 a a DT cord-026306-mkmrninv 217 36 large large JJ cord-026306-mkmrninv 217 37 - - HYPH cord-026306-mkmrninv 217 38 scale scale NN cord-026306-mkmrninv 217 39 hypertextual hypertextual NN cord-026306-mkmrninv 217 40 Web web NN cord-026306-mkmrninv 217 41 search search NN cord-026306-mkmrninv 217 42 engine engine NN cord-026306-mkmrninv 217 43 A a DT cord-026306-mkmrninv 217 44 new new JJ cord-026306-mkmrninv 217 45 status status NN cord-026306-mkmrninv 217 46 index index NN cord-026306-mkmrninv 217 47 derived derive VBN cord-026306-mkmrninv 217 48 from from IN cord-026306-mkmrninv 217 49 sociometric sociometric JJ cord-026306-mkmrninv 217 50 index index NN cord-026306-mkmrninv 217 51 Authoritative authoritative JJ cord-026306-mkmrninv 217 52 sources source NNS cord-026306-mkmrninv 217 53 in in IN cord-026306-mkmrninv 217 54 a a DT cord-026306-mkmrninv 217 55 hyperlinked hyperlinked JJ cord-026306-mkmrninv 217 56 environment environment NN cord-026306-mkmrninv 217 57 Eigenvector eigenvector NN cord-026306-mkmrninv 217 58 - - HYPH cord-026306-mkmrninv 217 59 like like JJ cord-026306-mkmrninv 217 60 measures measure NNS cord-026306-mkmrninv 217 61 of of IN cord-026306-mkmrninv 217 62 centrality centrality NN cord-026306-mkmrninv 217 63 for for IN cord-026306-mkmrninv 217 64 asymmetric asymmetric JJ cord-026306-mkmrninv 217 65 relations relation NNS cord-026306-mkmrninv 217 66 Communication communication NN cord-026306-mkmrninv 217 67 patterns pattern NNS cord-026306-mkmrninv 217 68 in in IN cord-026306-mkmrninv 217 69 task task NN cord-026306-mkmrninv 217 70 - - HYPH cord-026306-mkmrninv 217 71 oriented orient VBN cord-026306-mkmrninv 217 72 groups group NNS cord-026306-mkmrninv 218 1 A a DT cord-026306-mkmrninv 218 2 set set NN cord-026306-mkmrninv 218 3 of of IN cord-026306-mkmrninv 218 4 measures measure NNS cord-026306-mkmrninv 218 5 of of IN cord-026306-mkmrninv 218 6 centrality centrality NN cord-026306-mkmrninv 218 7 based base VBN cord-026306-mkmrninv 218 8 upon upon IN cord-026306-mkmrninv 218 9 betweenness betweenness NN cord-026306-mkmrninv 218 10 Graphs Graphs NNP cord-026306-mkmrninv 218 11 and and CC cord-026306-mkmrninv 218 12 cooperation cooperation NN cord-026306-mkmrninv 218 13 in in IN cord-026306-mkmrninv 218 14 games game NNS cord-026306-mkmrninv 219 1 A a DT cord-026306-mkmrninv 219 2 model model NN cord-026306-mkmrninv 219 3 of of IN cord-026306-mkmrninv 219 4 influence influence NN cord-026306-mkmrninv 219 5 in in IN cord-026306-mkmrninv 219 6 a a DT cord-026306-mkmrninv 219 7 social social JJ cord-026306-mkmrninv 219 8 network network NN cord-026306-mkmrninv 219 9 Power Power NNP cord-026306-mkmrninv 219 10 in in IN cord-026306-mkmrninv 219 11 network network NN cord-026306-mkmrninv 219 12 structures structure NNS cord-026306-mkmrninv 219 13 Multilayer Multilayer NNP cord-026306-mkmrninv 219 14 networks network VBZ cord-026306-mkmrninv 219 15 Centrality centrality NN cord-026306-mkmrninv 219 16 in in IN cord-026306-mkmrninv 219 17 interconnected interconnect VBN cord-026306-mkmrninv 219 18 multilayer multilayer NN cord-026306-mkmrninv 219 19 networks network NNS cord-026306-mkmrninv 219 20 Influence influence NN cord-026306-mkmrninv 219 21 assessment assessment NN cord-026306-mkmrninv 219 22 in in IN cord-026306-mkmrninv 219 23 multiplex multiplex NN cord-026306-mkmrninv 219 24 networks network NNS cord-026306-mkmrninv 219 25 using use VBG cord-026306-mkmrninv 219 26 social social JJ cord-026306-mkmrninv 219 27 choice choice NN cord-026306-mkmrninv 219 28 rules rule NNS cord-026306-mkmrninv 219 29 On on IN cord-026306-mkmrninv 219 30 the the DT cord-026306-mkmrninv 219 31 Dempster Dempster NNP cord-026306-mkmrninv 219 32 - - HYPH cord-026306-mkmrninv 219 33 Shafer Shafer NNP cord-026306-mkmrninv 219 34 Framework Framework NNP cord-026306-mkmrninv 219 35 and and CC cord-026306-mkmrninv 219 36 New New NNP cord-026306-mkmrninv 219 37 Combination Combination NNP cord-026306-mkmrninv 219 38 Rules Rules NNPS cord-026306-mkmrninv 219 39 Combination Combination NNP cord-026306-mkmrninv 219 40 of of IN cord-026306-mkmrninv 219 41 evidence evidence NN cord-026306-mkmrninv 219 42 in in IN cord-026306-mkmrninv 219 43 Dempster Dempster NNP cord-026306-mkmrninv 219 44 - - HYPH cord-026306-mkmrninv 219 45 Shafer Shafer NNP cord-026306-mkmrninv 219 46 theory theory NN cord-026306-mkmrninv 220 1 The the DT cord-026306-mkmrninv 220 2 choice choice NN cord-026306-mkmrninv 220 3 of of IN cord-026306-mkmrninv 220 4 generalized generalized JJ cord-026306-mkmrninv 220 5 Dempster Dempster NNP cord-026306-mkmrninv 220 6 - - HYPH cord-026306-mkmrninv 220 7 Shafer Shafer NNP cord-026306-mkmrninv 220 8 rules rule VBZ cord-026306-mkmrninv 220 9 for for IN cord-026306-mkmrninv 220 10 aggregating aggregate VBG cord-026306-mkmrninv 220 11 belief belief NN cord-026306-mkmrninv 220 12 functions function NNS cord-026306-mkmrninv 220 13 General general JJ cord-026306-mkmrninv 220 14 schemes scheme NNS cord-026306-mkmrninv 220 15 of of IN cord-026306-mkmrninv 220 16 combining combine VBG cord-026306-mkmrninv 220 17 rules rule NNS cord-026306-mkmrninv 220 18 and and CC cord-026306-mkmrninv 220 19 the the DT cord-026306-mkmrninv 220 20 quality quality NN cord-026306-mkmrninv 220 21 characteristics characteristic NNS cord-026306-mkmrninv 220 22 of of IN cord-026306-mkmrninv 220 23 combining combine VBG cord-026306-mkmrninv 220 24 Toward toward IN cord-026306-mkmrninv 220 25 an an DT cord-026306-mkmrninv 220 26 axiomatic axiomatic JJ cord-026306-mkmrninv 220 27 definition definition NN cord-026306-mkmrninv 220 28 of of IN cord-026306-mkmrninv 220 29 conflict conflict NN cord-026306-mkmrninv 220 30 between between IN cord-026306-mkmrninv 220 31 belief belief NN cord-026306-mkmrninv 220 32 functions function NNS cord-026306-mkmrninv 221 1 The the DT cord-026306-mkmrninv 221 2 application application NN cord-026306-mkmrninv 221 3 of of IN cord-026306-mkmrninv 221 4 conflict conflict NN cord-026306-mkmrninv 221 5 measure measure NN cord-026306-mkmrninv 221 6 to to IN cord-026306-mkmrninv 221 7 estimating estimate VBG cord-026306-mkmrninv 221 8 incoherence incoherence NN cord-026306-mkmrninv 221 9 of of IN cord-026306-mkmrninv 221 10 analyst analyst NN cord-026306-mkmrninv 221 11 's 's POS cord-026306-mkmrninv 221 12 forecasts forecast NNS cord-026306-mkmrninv 221 13 about about IN cord-026306-mkmrninv 221 14 the the DT cord-026306-mkmrninv 221 15 cost cost NN cord-026306-mkmrninv 221 16 of of IN cord-026306-mkmrninv 221 17 shares share NNS cord-026306-mkmrninv 221 18 of of IN cord-026306-mkmrninv 221 19 russian russian JJ cord-026306-mkmrninv 221 20 companies company NNS cord-026306-mkmrninv 222 1 The the DT cord-026306-mkmrninv 222 2 contradiction contradiction NN cord-026306-mkmrninv 222 3 between between IN cord-026306-mkmrninv 222 4 belief belief NN cord-026306-mkmrninv 222 5 functions function NNS cord-026306-mkmrninv 222 6 : : : cord-026306-mkmrninv 222 7 its -PRON- PRP$ cord-026306-mkmrninv 222 8 description description NN cord-026306-mkmrninv 222 9 , , , cord-026306-mkmrninv 222 10 measurement measurement NN cord-026306-mkmrninv 222 11 , , , cord-026306-mkmrninv 222 12 and and CC cord-026306-mkmrninv 222 13 correction correction NN cord-026306-mkmrninv 222 14 based base VBN cord-026306-mkmrninv 222 15 on on IN cord-026306-mkmrninv 222 16 generalized generalized JJ cord-026306-mkmrninv 222 17 credal credal JJ cord-026306-mkmrninv 222 18 sets set NNS cord-026306-mkmrninv 222 19 On on IN cord-026306-mkmrninv 222 20 the the DT cord-026306-mkmrninv 222 21 conflict conflict NN cord-026306-mkmrninv 222 22 measures measure NNS cord-026306-mkmrninv 222 23 agreed agree VBD cord-026306-mkmrninv 222 24 with with IN cord-026306-mkmrninv 222 25 the the DT cord-026306-mkmrninv 222 26 combining combining NN cord-026306-mkmrninv 222 27 rules rule NNS cord-026306-mkmrninv 222 28 Identifying identify VBG cord-026306-mkmrninv 222 29 influential influential JJ cord-026306-mkmrninv 222 30 nodes node NNS cord-026306-mkmrninv 222 31 in in IN cord-026306-mkmrninv 222 32 weighted weighted JJ cord-026306-mkmrninv 222 33 network network NN cord-026306-mkmrninv 222 34 based base VBN cord-026306-mkmrninv 222 35 on on IN cord-026306-mkmrninv 222 36 evidence evidence NN cord-026306-mkmrninv 222 37 theory theory NN cord-026306-mkmrninv 222 38 and and CC cord-026306-mkmrninv 222 39 local local JJ cord-026306-mkmrninv 222 40 structure structure NN cord-026306-mkmrninv 223 1 The the DT cord-026306-mkmrninv 223 2 transferable transferable JJ cord-026306-mkmrninv 223 3 belief belief NN cord-026306-mkmrninv 223 4 model model NN cord-026306-mkmrninv 224 1 A a DT cord-026306-mkmrninv 224 2 value value NN cord-026306-mkmrninv 224 3 for for IN cord-026306-mkmrninv 224 4 n n NN cord-026306-mkmrninv 224 5 - - HYPH cord-026306-mkmrninv 224 6 person person NN cord-026306-mkmrninv 224 7 games game NNS cord-026306-mkmrninv 224 8 Acknowledgements acknowledgement NNS cord-026306-mkmrninv 224 9 . . . cord-026306-mkmrninv 225 1 The the DT cord-026306-mkmrninv 225 2 article article NN cord-026306-mkmrninv 225 3 was be VBD cord-026306-mkmrninv 225 4 prepared prepare VBN cord-026306-mkmrninv 225 5 within within IN cord-026306-mkmrninv 225 6 the the DT cord-026306-mkmrninv 225 7 framework framework NN cord-026306-mkmrninv 225 8 of of IN cord-026306-mkmrninv 225 9 the the DT cord-026306-mkmrninv 225 10 Basic Basic NNP cord-026306-mkmrninv 225 11 Research Research NNP cord-026306-mkmrninv 225 12 Program Program NNP cord-026306-mkmrninv 225 13 at at IN cord-026306-mkmrninv 225 14 the the DT cord-026306-mkmrninv 225 15 National National NNP cord-026306-mkmrninv 225 16 Research Research NNP cord-026306-mkmrninv 225 17 University University NNP cord-026306-mkmrninv 225 18 Higher Higher NNP cord-026306-mkmrninv 225 19 School School NNP cord-026306-mkmrninv 225 20 of of IN cord-026306-mkmrninv 225 21 Economics Economics NNP cord-026306-mkmrninv 225 22 ( ( -LRB- cord-026306-mkmrninv 225 23 HSE HSE NNP cord-026306-mkmrninv 225 24 University University NNP cord-026306-mkmrninv 225 25 ) ) -RRB- cord-026306-mkmrninv 225 26 and and CC cord-026306-mkmrninv 225 27 supported support VBD cord-026306-mkmrninv 225 28 within within IN cord-026306-mkmrninv 225 29 the the DT cord-026306-mkmrninv 225 30 framework framework NN cord-026306-mkmrninv 225 31 of of IN cord-026306-mkmrninv 225 32 a a DT cord-026306-mkmrninv 225 33 subsidy subsidy NN cord-026306-mkmrninv 225 34 by by IN cord-026306-mkmrninv 225 35 the the DT cord-026306-mkmrninv 225 36 Russian Russian NNP cord-026306-mkmrninv 225 37 Academic Academic NNP cord-026306-mkmrninv 225 38 Excellence Excellence NNP cord-026306-mkmrninv 225 39 Project Project NNP cord-026306-mkmrninv 225 40 ' ' '' cord-026306-mkmrninv 225 41 5 5 CD cord-026306-mkmrninv 225 42 - - SYM cord-026306-mkmrninv 225 43 100 100 CD cord-026306-mkmrninv 225 44 ' ' '' cord-026306-mkmrninv 225 45 . . . cord-026306-mkmrninv 226 1 This this DT cord-026306-mkmrninv 226 2 work work NN cord-026306-mkmrninv 226 3 is be VBZ cord-026306-mkmrninv 226 4 also also RB cord-026306-mkmrninv 226 5 supported support VBN cord-026306-mkmrninv 226 6 by by IN cord-026306-mkmrninv 226 7 the the DT cord-026306-mkmrninv 226 8 Russian Russian NNP cord-026306-mkmrninv 226 9 Foundation Foundation NNP cord-026306-mkmrninv 226 10 for for IN cord-026306-mkmrninv 226 11 Basic Basic NNP cord-026306-mkmrninv 226 12 Research Research NNP cord-026306-mkmrninv 226 13 under under IN cord-026306-mkmrninv 226 14 grant grant NN cord-026306-mkmrninv 227 1 No no DT cord-026306-mkmrninv 227 2 18 18 CD cord-026306-mkmrninv 227 3 - - HYPH cord-026306-mkmrninv 227 4 01 01 CD cord-026306-mkmrninv 227 5 - - HYPH cord-026306-mkmrninv 227 6 00877a 00877a CD cord-026306-mkmrninv 227 7 . . .