内容美赛2014年mcmc类

InterdisciplinaryContestInofBeItKnownThatTheTeamSijiaJiangYukeZhuRuijieHeWithFacultyShuishengXidianD.ChrisArney,Contest

WasDesignatedOutstandingTinaR.Hartley,TinaR.Hartley,Head Forofficeuseonly

TeamControlC

ForofficeuseonlyMethodsofMeasuringInfluenceUsingNetworkInthispaper,webuildthenetworkmodeltomeasuretheimpactofresearchers,papersandsoon.Wefirstusethenetworkmodeltoevaluatetheimpctofresearchers,consideringresearchersasthenodes,andusingsidestodescribecollaboratonamongresearchers.Wethenproposetheconceptofimportancedegreeandinfluencedegree.Theyareallthepropertiesofnodes.Importancedegreedepictsanode’sownweightinthenetwork,whileinfluencedegreeestimatesanode’stotalnfluencethatmutualimpactamongnodesisincluded.Basedonthecomprehensiveconsiderationoftheclusteringcoefficientanddegree,weputforwardanewideatomeasureanode’simportancedegree.ThencombiningwithPageRankalgorithm,wecanevaluatetheinfluencedegreeofeverynodeinthenetwork.WecanfindALON,NOGAMisthemostinfluentialresearcher.Byyzingtheproprtiesofnodes,wefindthatforageneralresearcher,she/heshouldextenditscollaborativenetworkasgreatlyaspossible,especiallypartnerresearcherswithhighimportancedegree.Second,imitatingpreviousmethodology,webuildthemodeltoevaluatetheimpactofpapers.Weconcludethatfactorsdeterminingapaper’sinfluencecontainthreeindexes:thefirstauthor’sH-value,thejournal’sImpactFactorandcitedindexwhichistheconceptwedefinetodepicttheinfluencedegreeofapaperintheaspectofcitation.Referringtothepreviousidea,weconstructanewnetworkreflectingcitationrelationshipamongpapers,thenwecanobtainthecitedindexofeverypaper.Afterhavingcollectedthevalueofanothertwoindexes,weuseAHPtodeterminetheweightofthreefactors,andfinallyevaluatethetotalinfluenceofapapersuccessfully.WefindthatthepaperStatisticalmechanicsofcomplexnetworksismostinfluential.Afterthatweviewtheotherfieldsinsteadoftheacademicareatoextendourmodel.Weapplyournetworkmodelmeasuremoviestars’influence.WeselectagreatlyinfluentialmoviestartorecethestatusofErdös,andconstructthecooperatingnetworkamongmoviestars.Havingobtainedinfluencedegreeofstars,therankingofinfluenceofmoviestarsmaintainedahighlyconsistentwithreality.Thisisproofthatourmodelisfeasible.Thenwediscussourmodel’sapplicationforacademic,militaryandSNSfieldsroughly.Finally,wemakeasensitivity ysisforourmodel,anddiscusstheimpactofthechangingofnodesandthepapers’feedbackofcitationrelationshipontheresults.Throughprevious ysis,wecanseethatourmodelcanbeappliedtomanyfiles,soithasarelativelyhighgeneralization.. Introduction................................. Background............................... Ourwork................................ Assumptions................................. SymbolDescription............................. Theinfluenceofresearchers......................... Modelone:themeasurementofnodes’importancedegreemodelonnetworktheory................ . ...... EvaluatingtheimportanceofresearcheronlybyNodedegree Evaluatingtheimportancedegreeofresearchersusingclusteringcoefficient............ .............. Theevaluationmodelbasedontheclusteringcoefficientandgree.............. ........... Modeltwo:themeasurementofnodes’influencedegreemodelonPageRankalgorithm. . ................... AnintroductiontoPageRank ................ ThePageRankevaluationmodelbasedontheimportance ysis:someinterestingdata................. Theinfluenceof Thecitingnetworkof prehensveevaluationmodelbasedon Model Applyingmodelstoaspecific ysisofmodels ysisofthecollaborative ysisoftheciting ysisofthe 感谢作者 28747XidianUniversityICM2014OutstandingPaperAdvisior：ShuishengJiangSijia，ZhuYuke，He Copyright2014@All AllRightsPage1ofDoyoubelievethateveryoneintheworldcanestablishcontactwithanyoneelsebyonlysix satmost?EventheU.S.andtheboatmanofVenice,oncefind-ingtheright ,theycanestablishconnection.Thefamoussixdegreesofseparationtheorylsusthataslongaswefindrightmedia,wecanbuildrelationshipbetweenanytwoseeminglyunrelatedentities.Thistheoryisstillapplicableinacademia.Someresearcherscanoftencompletesomehigh-qualitypapersthroughcooperation,whichisinseparablefromthestrongre-lationsamongthem.Inthisera,interdisciplinarystudyisveryprevalent,sotheresearchcapabilityofresearchersandacademicstandardsofthepaperareaffectedbymanyas-pectsofintricateacademicnetwork.Moreandmoreattentionhasbeenpaidtohowtojudgetheacademiclevelandthequalityofpapers.PaulErd¨sisalegendarymathematician.Inhishalf-centurycareerinscientificresearch,hehadmorethan500collaboratorsandpublishedmorethan1400academicpapers.Thereisnodoubtthatheisoneofthemosinfluntialfoundersinthestudyofinterdisciplinary.Peoplecanevendefineaconceptcalled”collaborativedistance”,andErd¨Erd¨Erd¨s2representstheresearcherswhohaddirectcooperationwithErd¨s1,andsoon.TostudytheinfluenceofresearcherswhohaddirectcooperationwithErd¨s(theswhoseErdo¨snumberisone),thispassageisinspiredbyPageRankusedinsearchengineandclusteringcoefficientwhichmeasurestheimportancedegreeofeachnodeinthenetwork,andestablishnetworkmodelbasedongraphtheory.Wegiveamethodologytoevaluatetheinfluenceofresearchersandpapers,andextendthismodeltoanotheraspects.OurFirst,theinfluenceofresearchersandtheimportanceofresearchersarebotharela-tivelyvagueconcept.Inordertogetaclearpictureoftheproblem,wethinkthatthreefactorsshouldbetakenintoconsiderationtomeasuretheinfluenceofoneresearcher:Theresearcher’sextensivedegreeinthefieldofcooperation,namelythenumberofpartners.Thetimesofcooperationwithotherresearcherswhohavestronginfluence.Inthispaper,itisthetimesofcooperationwithErdo¨s.

28747XidianUniversityICM2014OutstandingPaperAdvisior：ShuishengJiangSijia，ZhuYuke，HeRuijie

Page2ofTheacademiclevelofpartnerswhocooperatewiththeThemeasureoftheimportanceofaresearchpapershouldcontainthefollowingTheauthor’sinfluenceoftheresearchpaper’s,wecanmeasureitbyH-Thepopularityofthejournalwhichhavepublishedthisresearchpaper,wecanusethejournal’sImpactFactor(IF)toexpress.ThenumberofcitationbyotherOnthebasisofabovediscussion,toevaluatetheinfluenceofresearchersandresearcherpaper,andtopromoteittobeappliedintheactual,wemayboildownthetaskstothefollowingfourquestions:Bylimitingthesizeofnetworkandextractingthedata,buildacoauthornetworkofthe511researchersfromthefileErdos1andyzethepropertiesofthisnet-thenetwork,andthendoevaluationandrankingforthem.(Erdo¨sisnottheretoytheseroles.)Changetheobjectofstudyanddesignamodeltoevaluatethesignificanceofresearcherpaper.Considerhowyouwouldmeasuretherole,influence,orimpactofaspecificuniversity,department,orajournalinnetworkscience?Dorankingfortheimportanceofresearchpaperandcomparethedifferencebetweenthesetwomethodology.Collectdata,andextendpreviousmodelsandalgorithmstootherfieldsintheactualtoexaminetheiradaptability.DiscussthescienceandutilityofthemodelbuiltIfapaperwascitedmorethanonceinanotherpaper,weregarditasTheimportancedegreewemeasureisforTheaveragevalueofmeasurementindexesofpapersormoviestarscanreflecttheircurrentimpact.ThenumberofcooperationwithErd¨scanaffectaresearchersinfluencedegree,butwhenthenumberexceedacertainvalue,theaffectionwouldbetendtobeaTosomedegree,thequalityofonepaperisproportionaltothenumbercitedbyotherpapers. 28747XidianUniversityICM2014OutstandingPaperAdvisior：ShuishengZhouTeam# JiangSijia，ZhuYuke，HeRuijiePage3ofCopyright2014@AllRightsAllSymbolInthesection,weusesomesymbolsforconstructingthemodelas Theresearcherisimportancedegreeinthe Theresearcherisinfluencedegreeinthe TheH-indexofpaperis TheImpactFactorofpaperisEDeviationDegreebetweentheoldresultsE thenewrankingresultsafterdeletingnodeP.s:OthersymbolsinstructionswillbegivenintheTheinfluenceofBeforemodeling,toavoidambiguitywewilldefinethetwoconfusingTheimportancedegreeofanode:thenode’sinfluenceinthenetwork.Itmea-suresanode’sabilitytocommunicatewithneighbournodesandtobuildthecon-nectionamongdifferentnodesinthewholeTheinfluencedegreeofanode:Duetotheconnectionwithothernodes,thenodewasaffectedbyothernodesandthereforeitpossessesitsowncomprehensiveModelone:themeasurementofnodes’importancedegreemod-elbasedonnetworktheoryInordertomeasuretheinfluencedegreeofeachresearcher,accordingtographtheo-ry,wedefinethenodesasresearchersandthesidesasthepartnershipamong.Thus,weestablishnetworkmodelwhichcanreflecttheinterrelationamongthere-searchers.Tofacilitateunderstandingandfurtherysis,wegivetheschematicdia-gramofthenetworkmodel,showninFigure1.Wecanseethatthroughsmallscopeofcooperation,researcherspromotetheconnec-tivityofthewholenetwork,andcontributetotheconnectionamongseeminglyunrelated Figure1:Thediagramwhichdescribestherelationamong10researchers

Figure2:Afterdeletingnode8,thecon-nectivityofthegraphhasbeendestroyed.Toevaluatetheimportancedegreeofeachresearcherinthenetworkmodel,wediscussitsmeasuringmethodinthefollowingsection.EvaluatingtheimportanceofresearchersonlybyNodeAssumethatnetworkG=(V;E)isundirectedandconsistsof|V|=Nnodes|expressedki=Âj2G<0, :1InFigure1,node8hasthemostnodedegree,ork8=4.Ifdeleteit,asshowninFigure2,node7,9and10 eisolated,theconnectivityofthenetworkarebadlyaffected.Incontrast,itsimpactdegreedeclinelessifthedeletednodesdegreeisless.Therefore,thetyofnodes’degreerepresentstheimportanceofresearchers.But,isthenodeswhichhavethesamenumberofdegreehavethesameWeyzeitinthefollowing,asisshowninFigure3and4Inthepicture,node2and4havethesametiesofdegree.However,deletingnode2hasnoeffectontheconnectivityofthewholenetwork.Afterdeletingnode4,node5isseparated,andnode7,8,9,10losetheconnectionwithnode1,2,3,6.Thusitcanbeseenthatthenodeswhichhavethesamenumberofdegreedonotalwayshavethesameimpactdegree.Sowecanconcludethatnodedegreerepresentsthedirectconnectingabilitywithitsneighbornode,butitcannotreflectitsinfluenceontheconnectivityofthewhole Figure3:Theconditionofconnectionafterdeletingnode2.

Figure4:Theconditionofconnectionafterdeletingnode4network.Tolookforasuitablemethodtosolvethisproblem,weintroducetheconceptofclusteringcoefficient.kAssumethedegreeofnodeiisk,thenthe umtriangleformedbythekneigh-bournodesisC2,hypothesiseeirepresentsthenumberoftriangleformedbyanytwoneighbornodes,thenclusteringcoefficient[4]canbedefinedas:kci=k

Ingraphtheory,aclusteringcoefficientisameasureofthedegreetowhichnodesinagraphtendtoclustertogetherAndinthispassage,itdescribesthecooperationdegreebetweenaresearcherandhispartners.Byyzingthenode2and4intheFigure3and4,wefindbecauseofthenodedegreeofthemareboth3,the umtriangleformedbytheirneighbournodesare33.However,intheactualsituation,thetrianglenumberofnode2is2andnode4is0,soc2=2,c4=0.Theresultindicatesthatothernodeswhichhavecooperatedwithnode4havenoconnectionwitheachother.Node4iscrucialinconnectingothernodesandismoreimportantthannode2.3However,differentfromdegreeindex,clusteringcoefficientcanreflecttheconnec-tivityofneighbournodestosomeextent,butitcannotshowthescaleofneighbournodes.Hence,weshouldevaluatetheimportanceofnodesbyconsideringnodedegreeandclusteringcoefficientsynthetically.TheevaluationmodelbasedontheclusteringcoefficientandFirst,weconsidernodeAssumefiisthesumdegreeofitselfandneighbournodesfornodei,anditcanbeexpressedas:fi=ki+Â Wherekwisthedegreeofnodew,Giisthecollectionofnodei’sneighbournode.reflectstheinformationbetweenthenode’sdegreeanditsneighbourThen,weconsiderclusteringcoefficient.Assumegibe: j=1{fj}-fgi

j}-min{}f}ffwhereciistheclusteringcoefficientofnodei.Becauseclusteringcoefficientindicatetheconnectiondegreeamongneighbournodes,butcannotreflecttheirscale,socicanfinormalized.Shownasequation(4)[5],gialsoshowclosenessamongneighbourAssumepiistheimportancedegreeofnodei,toevaluatetheimportanceofnodessynthetically,wedealwithfipandgibythechemotacticfunction[5]u(x)= ,soweÂgettheimportancedegreepi

si= Nf

Nj=1 j=1Ontheotherhand,considereveryresearcherhasdifferenttimesofdirectcooperationwithErdo¨s,andthetimescanreflecttheimportanceofresearchertosomedegree.Sotofytheindex,weuseapiecewisefunctiontosimulatetheimpactofxdirectcooperationwithErdo¨sontheresearchers’importance,itisexpressedas:8<0.002x11,0<x< 0.2,x�Therefore,thecomprehensiveimportanceofeveryresearcherqi=Pi(x)+ Inordertosimplifythecalculation,weonlystudytheco-authornetworkoftheErd¨s1authors,thenwegettheqiof511researchersandlistthetoptenresearchersasshowninTable1.(Notethatthisrankingisnottheresearcherseventuallyinfluenceranking,buttheimportanceinthenetwork.)Table1:Therankingofresearchers’importancedegreeqCooperation152HARARY,23GRAHAM,RONALDBOLLOBAS,TUZA,FUREDI,SOS,VERAPACH,Bystatistics,Erd¨shadcooperated1671tmesintotalwiththe511researchersandtheaveragenumberofcollaboraivetimeis3yzingthedataaccordingtoTable1,wefindinmostcasesthatthetoptenresearchers’importancearethosewhocooperatedwithErd¨sfrequentlyandtheirfirstcooperationisveryearly.Thereasonableexna-tionforthisphenomenonisthattheirfrequentandearlycooperationhelpthemdevelopandgrowinthecollaborativenetwork,andtheirimportanceisirreceable.Wecallthiskindofgroup”oldresercher”.late(”youngresearcher”)cannotbuildamaturenetworkrelationship.TheirimportanceForexample,ifa”youngresearcher”cancooperatedwitha”oldresearcher”,she/hemaymakeabreakthroughandimprovetheirinfluencedegree.Therefore,itisnotthefinalindextoevaluatetheinfluence.Weneedtoestablishaobjectivemodeltoevaluatetheimpactinviewofthecooperationinfluenceontheresearcher.Modeltwo:themeasurementofnodes’influencedegreemodelbasedonPageRankalgorithmownimportancedegreeandinfluencedegreedeterminedbytheircollaborativenetwork,weintroducePageRankalgorithmtodealwiththisproblem.Becauseofitspowerfulretrievalfunctionandhighqualityretrievalserviceisoneofthemostpopularsearchengines.UsingitsPageRankalgorithmtocalculatethePageRankvaluesofeachwebpage,gettherankofthewebpagebybalancingthenumberoflinkstothesearchtargetandthequalityoftheselinks.ThehigherthevalueofPageRankis,thehighertherankhas[2].ThePageRankevaluationmodelbasedontheimportanceInsection4.1,we’vegotimportantdegreeofeveryresearchers,setaijistheimpor-tancedegreeofnodeitonodej,sowecangettheadjacentmatrixamongnodesinthenetwork,weuseAtoexpress:2 ··· A=6 ···a2n Where,aij

···80,iandj<:qi,iandjdontconnect.(i,j=0,1,2,...,

Todistributetheresearcher’simportanceequallytoresearcherswhocooperated,normalizeeachlineofthematrixsetthisnewmatrixbeA¯,thentransposeA¯andgetthematrixoftransitionprobabilityW,or: AssigneachresearcheraPageRankvaluexiitshouldbedeterminedbyhis(her)partners’importancedegreeqi.Inaotherword,oneresearcher’sinfluencedegreeisproportionaltoher/hispartners’importance.Setthecommonproportionalitycoefficientbel,wecangetthefollowinglinearNÂwijxj=li,(xi=qi,i=1,2,..., LetX=(x1,x2,...,x511)Tbecolumnvectorformedbytheeffectfromotherre-searchers.Throughmatrixmultiplication,equation(4.2.2)canbeexpressedas:WX=l Thuswecanobtainthe umpositiveeigenvaluesofthetransitionprobabilitymatrixxthecorrespondingnon-negativefeaturevectorXmax=(x1,x2,...,x511)T,sowegetresearchers’impactx1,x2,...xnandultimayinfluencerankings.Weonlylisttoptenresearchers,showninTable2.p1ALON,NOGA2GRAHAM,RONALD3BOLLOBAS,04RODL,5FUREDI,06TUZA,07HARARY,8SOS,VERA9SPENCER,JOELFAUDREE,RALPHJASPER, ysis:someinterestingWealreadyknowtheresearchers’importanceindexandinfluenceindexaretwod-ifferentevaluationcrterionsofmeasuringthelevelofscientificresearchers.Theformerreflectstheresearcher’sabilitytocontributetotheconnectioninthenetworkbycontact-ingotherresearchers,whilethelattershowstheresearcherisaffectedbyherself/himselfandher/hispartnersandcanchangethesefactorsintoher/hisoverallinfluence.Comparingtherankresultofthetwomethods,wefindthatthechangeofoverresearchers’rankingiswithin75.Inviewoftheirdifferenceofemphasis,itisHowever,yzingtheremainingdata,wefindsomeinterestingphenomenon,weshowitinTable3Intheabovetable,wedefinetheareaofyellowasstabledata,theareaofgreenaspositivedataandtheareaofredasnegativedata.Stabledata:we yzethetopfiveinfluenceofresearchersandfindtheirrankingiscloselytotheirimportanceranking.WeconcludetheinfluencedegreeoftheresearcherswithlargeimportancedegreeisalsoTable3:Theschematicdiagramofresearchers’

p- 1105GRAHAM,RONALD321BOLLOBAS,532440FUREDI,752PYBER,3TETALI,PRASAD22FISHBURN,PETERTENENBAUM,7STEIN,ALAN1SMITH,PAUL1MAXSEIN,11Positivedata:Someresearchers’influencedegreerankingimprovebymorethan250thantheirimportancedegreeranking,someevenimproveby351.TheircommonfeatureistheirfirstcooperationwithErdo¨sislate,sotheircooperationnetworkcannotdevelopmaturelyandtheirimportancedegreerankingislow.However,byooperaingfrequentlywithhighinfluenceresearchers,theirinflu-encedegreecanbepromoted.TakeFISHBURN,PETERCasanexample,noton-searcherswhoseimportancedegreeishigh(FUREDI,ZOLTAN,GRAHAM,RONALDLEWISandSPENCER,JOELHAROLD),sohisinfluencedegreerankinghavegreatlyimproved.Weconcludethatevenwithlowerimportancedegreeinthenetwork,onecanenhanceitsinfluencedegreebycooperatingwithhighlyin-fluentialresearchers.Negativedata:Wefindfourresearchers’influencedegreedropmorethan100.Investigatingtheirdata,wegettheirpartnersaremorethan20,butoverhalfofthemdon’tbelongtoErdo¨s1.Theresultshowsthattheresearcherwhocooperatelessfrequentlyhavelowinfluencedegree.Sowecandrawtheconclusionthataresearchercanimprovetheirinfluencebyenhanc-ingitsowncollaborativenetwork,andtheimportancedegreeofitspartnersysTeam#

28747XidianUniversityICM2014OutstandingPaperAdvisior：ShuishengJiangSijia，ZhuYuke，He Page11ofCopyright2014@AllRightsAllimportantroleinenhancingitsTheinfluenceof

Toevaluateresearchpapers’influence,wechoose15researchpapersinandusethemethodofthesection§4.Weestablishamodelwhichreflectsthein amongresearcherpapers.Undoubtedly,thebestwaytoevaluatetheinfluencedegreeofaresearchpaperisexaminingthequalityofthecontent.However,theredoesn’texistagreatanddirectmethodforit.Therefore,weneedtolookforindexestoevaluateindirectly.By-ysis,wethinkthefactorsthataffecttheinfluencedegreeofresearchpapersismainlymanifestedintwoaspects.Externalinfluencedegree:thecitingofapaperisanimportantindextomeasureitsinfluence.Byyzingtherelationofthemutualcitingofthese15papers,wecanbuildacitingnetworksimilartomodelone,andusePageRankalgorithmtoevaluateeverypaper’sinfluencedegree.Internalinfluencedegree:Itisalsoaffectedbyitsfirstauthor’slevelofscientificresearch,namelyHindex,andtheinfluenceofthejournal,namelyImpactFactor(IF).Sowechoosetheabovethreeindexestoevaluatepapers’influenceThecitingnetworkofFirstofall,differenfromnetworkrelationshipofresearchers,oneresearchpapercanonlycitethepaperpublishedbeforeitandthereisnorelationshipofcooperationbetweenthem.Nevertheless,oncected,itindicatesthisresearchpapergetstheaffirmationfromotherresearchers.Themoretheresearcherpaperiscited,thehigherinfluenceofthisresearcherpaperwillhave.Meanwhile,thequotercanalsobenefitfromitandimprovehis(her)paperimpact.Hence,wecanestablishfeedbackrelationshiplikeresearchers.Weestablishthenetworkrelationshipgraphamongresearchpapers.Thenodesrepresentresearchpapersandthesidesrepresentthefeedbackrelationshipamongresearchpapers(weassumethattheeffectsofinctionoftwopapersexistcitingrelationareequal),shownintheFigure5.UsingthePageRankalgorithminmodeltwo,wecangettheinfluencedegreeinthenetwork,wecallitpapercitedindex,setitber,whichmeasuresitscitedinfluence.Bycollectingdatafromauthoritativewebsite(suchasSCI,Scholar),weusethenumbercitedbyothersastheindextomeasuretheimportancedegreeqofeveryTeam#

Figure5:Thecitationnetworkamong

Page12ofSettheadjacencymatrixofthenodesinthenetworkbe ··a ···A=4

·<80iandjconnectThereinto,aij=:<q,iandjdon’tNormalizeAanduseequation11),wecangetrofthese15research

prehensiveevaluationmodelbasedonrcanonlyreflecttheeffectfrometernalelement.Toevaluatearesearchpaperover-all,wearedeterminedtouseAHPandcalculatetheweightofIF,Hindexandr.Wethinkthatintheprogressofmeasuringaresearchpaper,thefirstauthorshouldn’tbeconsideredtoomuch.Exceptthat,thecontributionofinternalfactorisgreaterthanexternalfactor.Sowesetthesizeofrelationshipofthethreefactors:IF>r>H.Bythisprinciple,wegivePairwisecomparison0 r B 4 1@1 Team#

Page13ofWetheninputthematrixintoYAAHPandcalculatetheweightofeachfactor:aIF0.5469,aH=0.1085,ar=Thefinalexpressionofevaluatingonepaper’sinfluencedegreeTi=aIFIFi+aHHi+arri Inthefollowing,wetesttheconsistencyoftheAHP.TheconsistencyindexCI=lxnshouldbecloseto0;wegetCI=TheconsistencyratioCR=CIshouldbelessthan0.1;WegetCR=0.02.ourdecisionmethoddisysperfectlyacceptableconsistencyandweightsareListthetopfiveinfluencedegree,showninTableTable4:Theschematicdiagramofpaprs’ r12 24 3 4 -57 -Inthefirstthreetasks,wehavesolvedtheproblemofmeasuringtheinfluencedegreeofresearchersandpapers.Ifweareabletogetenoughinformationaboutresearchpapersandresearchers,wecancreatearesearchdatabase.Ifwewanttoevaluatetheresearchstrengthofauniversityoradepartmentinacertainfield,weneedtolookfortheresearchersandtheresearchpapersinrecentyearsofthisorganization,theninquiretheirinfluenceinthedatabase.Finallywecandeterminethestrengthofitbychoosingasuitableevaluation(suchasTOPSIS).ModelInmodeloneandmodeltwo,usingthenetworkmodel,wefytheinfluenceofresearchersandpapers,showingthestrongabilityofourmodeltoevaluateacademicindex.Asamatterofafact,ourmodelscanbeappliedinvariousfieldsseeminglyhavenothingtodowithscience.Sointhefollowingsection,wewillemployournetworkmodeltoevaluatetheinfluenceof moviestars,andconsideritsextensionwidely. Copyright2014@All All Applyingmodelstoaspecific

Page14ofThecinemaofHongKongisoneofthethreemajorthreadsinthehistoryofChi-neselanguagecinema,alongsidethecinemaof,andthecinemaof.Fordecades,HongKongwasthethirdlargestmotionpictureindustryintheworldandthesecondlargestexporter.SoitisobviousthattheindustryofHongKong’scinemayssuchapredominateroleinandeventhewholeworldthatithasgreatlyprompt-edthedevelopmentofthecinemaindustryinand.TherearesomeilluminatedmoviestarsfromHongKong,suchasJackieChan,Tonyleungchiuwai,AndyLauandsoonwhoalsohaveagreatreputationaroundtheworld.[6]ForthefactthatTonyleungchiuwaihasaverymagnificentcinemacareer,includingbeingawardedtheGoldenHorsebestactornominationmorethanonce,wedecidetorecetheErdo¨sinthepreviousnetworkmodelwithhim,andthenqualifytherangeoftimeandtheregion,inorderingthatwecanconstructanewnetworkmodelbasedontheModel1whichcanbeusedtoassessamoviestar’sinfluencedegree.ForthefactthatTonyleungchiuwaihasaverymagnificentcinemacareer,includingbeingawardedtheGoldenHorsebestactornominationmorethanonce,wedecidetorecetheErdo¨sinthepreviousnetworkmodelwithhim,andthenqualifytherangeoftimeandtheregion,inorderingthatwecanconstructanewnetworkmodelbasedontheModel1whichcanbeusedtoassessamoviestar’sinfluencedegree.Besidesthat,wealsoneedanindextoassesseachactor’seffectonthe’sbox-office,andtheindexcanbeconsideredastheimportancedegreeModel1asabalanceofaactor’sstrength.Wenormalizetheaverageofthebox-officeofmovieswhereeachactorhasprticipatedinrecentfiveyearsasthenumberofthisbox-office’sinfluence.Table5:Theindexesofthemovieinfluencebox-1Zhou29Zhao34Andy5Zhang6Shu78Jet89Donnie98Jackie8LouisTeam

Page15ofPuttingthenumberintothematrixdepictingthecooperatedrelationshipbetweendifferentactors,wecangetthenumericaldataofthe31actorsinfluencedegreeusingthePageRankalgorithm.Rankingthestarsbytheinfluencedegree,wecangettheToptenshowninthechart:yzingtheTable5,wecanfindoutthatthebox-officeindicatingtheactorsstrengthhassomecontributiononthestarsinfluence,buttheactorscooperatingrela-tionshipnetworkalsoisanunignorablefactor.TakingZhangZiyiasanexample,whileshehasainferiorbox-officethanotherstars,wejustfindthecorrespondingnodehasahigherdegree,thatis,shehasmanymorecooperatedstarsthanothers,whichresultsinherhigherinfluencedegree.However,theJackieChanisanoddcase,hemainlypartici-patedintheactionmovies,addinghislackofcooperationwith overallinfluenceisnotthatsuperiordespiteofhisstrongbox-office.What’smore,thecurr