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1、英文翻译2010届电气工程及其自动化专业1006972班级姓名学号指导教师职称二О一二年二月十日342.3.NetworksmodelsTheobservationsdescribedintheexamplesofSection2.2haveclearlymotivatedtheintroductionofnewconceptsandmodels.Inthissection,wefocusonthemathematicalmodellingofnetw-orks,discussingsomesimpleandgenericmodelsfromthepointofviewofthei
2、rmotivation,const-ructionprocedureandsignificantproperties.FurtherdetailsonmodelscanbefoundinRefs.[2–4,7].2.3.1.RandomgraphsThesystematicstudyofrandomgraphswasinitiatedbyErdösandRényiin1959withtheorig-inalpurposeofstudying,bymeansofprobabilisticmethods,thepropertiesofgraphsasafunctionoftheincre
3、asingnumberofrandomconnections.Thetermrandomgraphreferstothedisorderednatureofthearrangementoflinksbetweendifferentnodes.Intheirfirstarticle,ErdösandRényiproposedamodeltogeneraterandomgraphswithNnodesandKlinks,thatwewillhenceforthcallErdösandRényi(ER)randomgraphsanddenoteasGERN,K.StartingwithNd
4、isconnectednodes,ERrandomgraphsaregeneratedbyconnectingcouplesofrandomlyselectednodes,prohibitingmultipleconne-ctions,untilthenumberofedgesequalsK[115].Weemphasizethatagivengraphisonlyoneoutcomeofthemanypossiblerealizations,anelementofthestatisticalensembleofallpossiblecombin-ationsofconnectio
5、ns.ForthecompletedescriptionofK,Nonewouldneedtodescribetheensemble34ofpossiblerealizations,thatis,inthematricialrepresentation,theensembleofadjacencymatrices[116].AnalternativemodelforERrandomgraphsconsistsinconnectingeachcoupleofnodeswithaprobability0
6、,denotedasGN,pandcontaininggraphswithdifferentoflinks:graphswithKlinkswillappearintheensemblewithaprobabilitypK34(1−p)N(N−1)/2−K[14,115,117].Thetwomodelshaveastronganalogy,respectively,withthecanonicalandgrandcanonicalensemblesinstatisticalmechanics[118],andcoincideinthelimitoflargeN[16].Notic
7、ethatthelimitN→∞istakenatfixedk,whichcorrespondstofixing2K/Ninthefirstmodelandp(N−1)inthesecondone.Althoughthefirstmodelseemstobemorepertinenttoapplications,analyticalcalculationsareeasierandusuallyareperformedinthesecondmodel.ERrandomgraph