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1、基于自相似性的复杂网络（Complexnetworksbasedonself-similarity）Complexnetworksbasedonself-similarityThisarticleiscontributedbyyixing13Theself-similaritystudyofcomplexnetworksbasedoncapacitydimensionsReporter:taoshaohuaguide:professorliuyuhuainMarch2006Theresultsofcomplexnetworkmodelarep
2、resentedinthispaper1.IntroductionIn1960,themathematicianErdosandRenyiproposedtherandomgraphtheory,andstudiedtherandomtopologymodelinthecomplexnetwork.Sincethen,ERmodelhasbeenthebasicmodelforstudyingthecomplexnetwork.However,recentstudieshavefoundthatmanyexperimentaldataobta
3、inedintherealnetworkarenotconsistentwiththerandomgraphmodel,soanewnetworkmodelisneededtoreasonablydescribetheactualnetwork.In1998,WattsandStrgatzproposedthesmallworld(WS)model[2],whichdepictsthecharacteristicsoftherealnetworkandsomelargeclusteringandshortaveragepathdistance
4、.Networkhasalsobeencountedintherealworld,howeverfewcontactwithlotsofconnections,andnumerouscontactswithonlyasmallamountofthecharacteristicsoftheconnection,thesecannotrationallyexplainthemwithrandomgraphmodel.In1999BarabasiandAlbertproposedascale-freemodel(BA)[3].TheBAmodelp
5、ointsouttwobasicprinciplesthatdeterminethescalemodeloftheInternetandtheworldwideweb:growthandpreferentialconnection.Althoughthesmallworldnetworkandthescale-freenetworkdepictthebasiccharacteristicsofthenetwork,theyarebasedonthepremiseofsimplifyingtherealnetwork.Therefore,iti
6、snecessarytodelveintocomplexnetworkmodelingtomakeitmorerealistic.Inthispaper,theself-similarityofthenetworkisproposed,andthenetworkisformedthroughnodeandnode,andthenodeandnodeareconnectedtogetherthroughsomecommonthread.Likethe"birdsofafeatherflocktogether"betweenpeople..2.B
7、riefintroductionofcomplexnetworkmodelAcomplexnetworkisalarge-scalenetworkwithcomplextopologicalstructureanddynamicbehavior.Itisagraphcomposedofalargenumberofnodesconnectedbyedges.Accordingtodifferenttopologicalstructurecomplexnetworkcanbedividedintorulenetwork,randomnetwork
8、,smallworldnetwork,noscalenetworkandsoon.2.1smallworldnetworkmodelIn1998,WattsandS
