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1、PHYSICALREVIEWE72,0171032005Nonlocalevolutionofweightedscale-freenetworksK.-I.Goh,B.Kahng,andD.KimSchoolofPhysicsandCenterforTheoreticalPhysics,SeoulNationalUniversityNS50,Seoul151-747,KoreaReceived3October2004;revisedmanuscriptreceived31March2005;published26July2005Weintroduc
2、ethenotionofgloballyupdatingevolutionforaclassofweightednetworks,inwhichtheweightofalinkischaracterizedbytheamountofdatapackettransportßowingthroughit.Bynotingthatthepackettransportoverthenetworkisdeterminednonlocally,thisapproachcanexplainthegenericnonlinearscalingbetweenthestren
3、gthandthedegreeofanode.Wedemonstratebyasimplemodelthatthestrength-drivenevolutionschemerecentlyintroducedcanbegeneralizedtoanonlinearpreferentialattachmentrule,generatingthepower-lawbehaviorsindegreeandinstrengthsimultaneously.DOI:10.1103/PhysRevE.72.017103PACSnumbers:89.75.Hc,0
4、5.40.a,87.23.KgNetworkresearchhasarisenastheinterdisciplinarysub-tativelydifferentorganizationofweightandnetworktopol-jectforstudyingcomplexsystems1Ð7.Althoughthebinaryogy.FortheSCN,thestrengthofanodescientistscaleson/offpictureofconnectivityhasbeenshowntobequitelinearlywit
5、hthedegree,thatis,informativeandledtoimportantprogressinourunderstand-skk.3ingofcomplexsystems,suchastheubiquityofpowerlawsinitsconnectivitypattern,thedegreedistribution8,pdkOntheotherhand,theWANexhibitsanonlinearscalingask−,onemayneedtoputastepforwardtodescribethemsk
6、k,4morerealistically.Theweightednetwork,inwhichlinksbe-tweennodesinthenetwork,ornodesthemselves,bearnon-with1.5.uniformweights,isoneofthemoststraightforwardgenerali-Later,Barrat,Barthelemy,andVespignaniBBVintro-zationsinthisdirection9Ð21.Theweightmayrepresentducedasimplee
7、volutionmodelforsuchweightednetworkstheintimacybetweenindividualsinsocialnetworks,orthe14.Basically,theBBVmodelissimilartotheBarabsi-bandwidthsofroutersandopticalcablesintheInternet.TheAlbertBAmodelofbinaryscale-freeSFnetwork8inweightednetworkcanbecharacterizedbythegeneral
8、izedspirit,containingthegrowthand
