Large-scale structure of time evolving citation networks

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1、Eur.Phys.J.B59,75–83(2007)THEEUROPEANDOI:10.1140/epjb/e2007-00271-7PHYSICALJOURNALBLarge-scalestructureoftimeevolvingcitationnetworksE.A.Leicht1,a,G.Clarkson2,K.Shedden3,andM.E.J.Newman1,41DepartmentofPhysics,UniversityofMichigan,AnnArbor,MI48109,USA2SchoolofInformation,UniversityofMichigan,An

2、nArbor,MI48109,USA3DepartmentofStatistics,UniversityofMichigan,AnnArbor,MI48109,USA4CenterfortheStudyofComplexSystems,UniversityofMichigan,AnnArbor,MI48109,USAReceived31May2007Publishedonline5October2007–
cEDPSciences,Societ`aItalianadiFisica,Springer-Verlag2007Abstract.Inthispaperweexamineanu

3、mberofmethodsforprobingandunderstandingthelarge-scalestructureofnetworksthatevolveovertime.Wefocusinparticularoncitationnetworks,networksofreferencesbetweendocumentssuchaspapers,patents,orcourtcases.Wedescribethreedifferentmethodsofanalysis,onebasedonanexpectation-maximizationalgorithm,onebased

4、onmodularityoptimization,andonebasedoneigenvectorcentrality.UsingthenetworkofcitationsbetweenopinionsoftheUnitedStatesSupremeCourtasanexample,wedemonstratehoweachofthesemethodscanrevealsignificantstructuraldivisionsinthenetworkandhow,ultimately,thecombinationofallthreecanhelpusdevelopacoherento

5、verallpictureofthenetwork’sshape.PACS.89.75.HcNetworksandgenealogicaltrees–89.75.FbStructuresandorganizationincomplexsystems–89.70.+cInformationtheoryandcommunicationtheory1IntroductionInadirectednetworktheadjacencymatrixis,ingeneral,asymmetric.Thephysicscommunityhasinrecentyearsdevotedcon-Ase

6、condfeatureofcitationnetworksisthattheysiderableattentiontothestudyofnetworks,includ-evolveovertimeasnewdocumentsarecreated.Theevo-ingsocialnetworks,biologicalnetworks,informationnet-lutionofthenetworktakesaspecialform,inthatverticesworks,andothers[1–3].Manyofthesenetworksalsohaveandedgesaread

7、dedtothenetworkataspecifictimelonghistoriesofstudyinotherfields.Citationnetworks,andcannotberemovedlater.Thispermanenceofver-whicharetheprincipalfocusofthispaper,havebeenticesandedgesmeansthatthestructureofthenetworkstudiedquantitativelya