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1EvolutionaryModelsandDynamicalPropertiesofComplexNetworksName:JianguoLiuUniversityofShanghaiforScienceandTechnology2010-3-242Outline1.ComplexnetworksanalysisbyCitespace2.Networkevolutionmodels3.Dynamicalpropertiesonscale-freenetworks4.Personalizedrecommendation31999年-2010年发表的以“complexnetworks”为主题词的SCI论文数020040060080010001200199920012003200520072009publishedSCIpapers4Citespace软件介绍CiteSpace：由美国德雷赛尔大学信息科学与技术学院的陈超美开发。该程序可以登录到cluster.cis.drexel.edu/~cchen/citespace后免费使用。利用Citespace寻找某一学科领域的研究进展和当前的研究前沿，及其对应的基础知识。5复杂网络论文作者合作网(1999-2010)6复杂网络研究小组状况(1999-2010)7复杂网络各个国家研究状况(1999-2010)8利用引文分析观察当前的研究热点(1999-2010)9Topcitedauthors(1999-2010)10各研究领域之间的关系(1999-2010)11个性化推荐的知识图谱12Topcitedauthors13目前的研究热点14Outline1.Backgroundintroduction2.Networkevolutionmodels3.Dynamicalpropertiesonscale-freenetworks4.Personalizedrecommendation152.Scale-freeNetworkEvolutionModels1.Multistagerandomgrowingsmall-worldnetworkswithpower-lawdegreedistribution2.Growingscale-freenetworkmodelwithtunableassortativecoefficient3.Self-learningmutualselectionmodelforweightednetworks4.Randomevolvingnetworksunderthediameteranddverageconnectivityconstraint162.1.Multistagerandomgrowingsmall-Worldnetworkswithpower-lawdegreedistributionLiuJian-Guo,DangYan-ZhongandWangZhong-Tuo,ChinesePhysicsLetters23(3)746-749(2006)•Onenodeisaddedineachtimestep；•Selectthenodeuaccordingtothepreferentialmechanism；•Selectaneighbornodeofnodeu；17181.Onenodeisaddedineachtimestep；2.Selectthenodeuaccordingtothepreferentialmechanism；3.Selectaneighbornodeofnodeuaccordingtops；2.2.Growingscale-freenetworkmodelwithtunableassortativecoefficientQiangGuo,TaoZhou,Jian-GuoLiuetal.,PhysicaA371814-822(2006)1920Twoparameters:attractivefactorp,thenumberofcandidatesm2.3Self-learningmutualselectionmodelforweightednetworksJian-GuoLiuetal.,DCDISBSupplement,ComplexNetworks,14(S7)33-36,(2007).11jijkksapsassp123412345m=21234521222.4RandomEvolvingNetworksUndertheDiameterandAverageConnectivityConstraintThegrowthofrandomnetworksundertheconstraintthatthediameter,definedastheaverageshortestpathlengthbetweenallnodes,andtheaverageconnectivityremainsapproximatelyconstantisstudied.Weshowedthat,ifthenetworkmaintainstheformofitsdegreedistributionandthemaximaldegreeisaN-dependentcutofffunction,thenthedegreedistributionwouldbeapproximatelypower-lawwithanexponentbetween2and3.Jian-GuoLiuetal.,JournalofSystemScienceandSystemEngineering16(1)107-112(2007).23MotivationInthebiologicalnetworks,theconstantdiametermayberelatedtoimportantpropertiesofthesebiologicalnetworks,suchasthespreadandspeedofresponsestoperturbations.IntheInternetbackbonenetwork,theaveragedistanceisoneofthemostimportantfactorstomeasuretheefficiencyofcommunicationnetwork,anditplaysasignificantroleinmeasuringthetransmissiondelay.Theseconstraintscanbethoughtofastheenvironmentalpressures,whichwouldselecthighlyefficientstructuretoconveythepacketsinit.24Motivation25ConstructionofthemodelTheexpressionforthediameterdofarandomnetworkwitharbitrarydegreedistributionwasdevelopedWhereistheaveragedegree,26InordertoseekadegreedistributionthatmaintainsitsdistributionandhasanapproximatelyconstantdiameterindependentofN.TheparameterNcanbeaccomplishedbyimposingaN-dependentcutofffunction27Thedistributionp(k)canbedeterminedbywritingthisequationforandAlgebraicmanipulationyieldstherelation28Usinganintegralapproximation,amoreexplicitformulationcanbewrittenasfollowing.29Whenthenumericallycalculateddegreedistributionsforvariousvaluesof30DiscussionofparttwoWehavepresentedareasonfortheexistenceofpower-lawdegreedistributionunderthediameterconstraintobservedintheInternetbackbonenetworkwherethereareevolutionarypressurestomaintainitsdiameter.Ouranalysisshowsthat,ifthemaximaldegreeisaN-dependentcutofffunction,theformofarobustnetworkdegreedistributionshouldbepowerlawtomaintainitsdiameter,whiletheaverageconnectivitypernodeaffectthedistributionexponentslightly.31Outline1.Backgroundintroduction2.Networkevolutionmodels3.Dynamicalpropertiesoncomplexnetworks4.Personalizedrecommendation323.1Structuraleffectsonsynchronizabilityofscale-freenetworks333.1HowtomeasurethesynchronizabilityWhereQistheratiooftheeigenvalues.ThesynchronizabilitywouldbeincreasedasQdecreases,viceverse.34Theedgeexchangemethodisintroducedtoadjustthenetworkstructure,andthetabusearchalgorithmisusedtominimizetheeigenvalueratioQminQiangGuo,LiuJian-Guo,etal,ChinesePhysicsLetters24(8)(2007)2437-2440.35Insummary,usingthetabuoptimalalgorithm,wehaveoptimizednetworksynchronizabilitybychangingtheconnectionpatternbetweendifferentpairsofnodeswhilekeepingthedegreedistribution.Startingfromscale-freenetworks,wehavestudiedthedependencebetweenthestructuralcharacteristicsandsynchronizability.Thenumericalresultssuggestthatascale-freenetworkwithshorterpathlength,lowerdegreeofclustering,anddisassortivepatterncanbeeasilysynchronized.363.1StructuraleffectsonsynchronizabilityminmaxCombiningthetabusearch(TS)algorithmandtheedgeexchangemethod,weenhanceandweakenthesynchronizabilityofscale-freenetworkswithdegreesequencefixedtofindthestructura