电气工程及其自动化专业毕业设计（论文）外文翻译

《电气工程及其自动化专业毕业设计（论文）外文翻译》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。

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