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1、时间序列分析方法研究复杂网络谱结构TemporalSeriesAnalysisApproachtoSpectraofComplexNetworksHuijieYang??,FangcuiZhao,LongyuQi,BeilaiHuSchoolofPhysics,NankaiUniversity,Tianjin300071,ChinaAbstractThespacingofnearestlevelsofthespectrumofacomplexnetworkcanberegardedasatimeseries.JointuseofMulti-fractalDetrend
2、edFluctuationApproach(MF-DFA)andDiffusionEntropy(DE)isemployedtoextractcharacteristicsfromthistimeseries.FortheWS(WattsandStrogatz)small-worldmodel,thereexistacriticalpointatrewiringprobability37><2.0=rp.Foranetworkgeneratedintherange3<2.00????rp,thecorrelationexponentisintherangeof64.1
3、~0.1.Abovethiscriticalpoint,allthenetworksbehavesimilarwiththatat1=rp.FortheERmodel,thetimeseriesbehaveslikeFBM(fractionalBrownianmotion)noiseatNpER/1=.FortheGRN(growingrandomnetwork)model,thevaluesofthelong-rangecorrelationexponentareintherangeof83.0~74.0.FormostoftheGRNnetworksthePDFo
4、faconstructedtimeseriesobeysaGaussianform.InthejointuseofMF-DFAandDE,theshufflingprocedureinDEisessentialtoobtainareliableresult.PACSnumber(s):89.75.-k,05.45.-a,0<2.60.-x_______________________________________________________________________________.paper.edu1I.INTRODUCTIONDetailedinves
5、tigationsindicatethatreal-worldnetworkshavehighlydistinctivestatisticalsignaturesveryfarfromrandomnetwork[1].Twoclassesofmodels,calledthesmall-worldgraphsandthescale-freenetworks,areproposedtocapturetheclusteringandthepower-lawdegreedistributionpresentinmanyrealnetworks,respectively[<2-
6、5].However,mostanalyseshavebeenconfinedtocapturethestaticstructuralproperties,e.g.,degreedistribution,shortestconnectingpaths,clusteringcoefficients,etc.Capturingtheglobalcharacteristicsofcomplexnetworksisanessentialroleatpresenttime.Anotherproblemisthelackofsuitabletechniques,whichleav
7、esalargegapinourcapturingthebasicpropertiescomprehensivelyandunderstandingnetworkstheoretically.Thus,anotherimportantroleistouseconceptsortechniquesdevelopedinotherfieldstocharacterizecomplexnetworks.Itisdemonstratedinextensiveliteraturethatthepropertiesofgraphsandtheassociated
