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1、英文翻译2010届电气工程及其自动化专业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,discussingsomesimpleandgeneric
2、modelsfromthepointofviewoftheirmotivation,const-ructionprocedureandsignificantproperties.FurtherdetailsonmodelscanbefoundinRefs.[2–4,7].2.3.1.RandomgraphsThesystematicstudyofrandomgraphswasinitiatedbyErdösandRényiin1959withtheorig-inalpurposeofstudying,bymea
3、nsofprobabilisticmethods,thepropertiesofgraphsasafunctionoftheincreasingnumberofrandomconnections.Thetermrandomgraphreferstothedisorderednatureofthearrangementoflinksbetweendifferentnodes.Intheirfirstarticle,ErdösandRényiproposedamodeltogeneraterandomgraphsw
4、ithNnodesandKlinks,thatwewillhenceforthcallErdösandRényi(ER)randomgraphsanddenoteasGERN,K.StartingwithNdisconnectednodes,ERrandomgraphsaregeneratedbyconnectingcouplesofrandomlyselectednodes,prohibitingmultipleconne-ctions,untilthenumberofedgesequalsK[115].W
5、eemphasizethatagivengraphisonlyoneoutcomeofthemanypossiblerealizations,anelementofthestatisticalensembleofallpossiblecombin-ationsofconnections.ForthecompletedescriptionofK,Nonewouldneedtodescribetheensemble34ofpossiblerealizations,thatis,inthematricialrepr
6、esentation,theensembleofadjacencymatrices[116].AnalternativemodelforERrandomgraphsconsistsinconnectingeachcoupleofnodeswithaprobability0
7、rintheensemblewithaprobabilitypK34(1−p)N(N−1)/2−K[14,115,117].Thetwomodelshaveastronganalogy,respectively,withthecanonicalandgrandcanonicalensemblesinstatisticalmechanics[118],andcoincideinthelimitoflargeN[16].NoticethatthelimitN→∞istakenatfixedk,whichcorres
8、pondstofixing2K/Ninthefirstmodelandp(N−1)inthesecondone.Althoughthefirstmodelseemstobemorepertinenttoapplications,analyticalcalculationsareeasierandusuallyareperformedinthesecondmodel.ERrandomgraphsarethe