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1、UniversalBehaviorofLoadDistributioninScale-freeNetworksK.-I.Goh,B.Kahng,andD.KimSchoolofPhysicsandCenterforTheoreticalPhysics,SeoulNationalUniversity,Seoul151-747,Korea(February1,2008)Westudyaproblemofdatapackettransportinscale-freenetworkswhosedegreedistributionfollowsapower-lawwith
2、theexponentγ.Load,orbetweennesscentralityofavertexistheaccu-mulatedtotalnumberofdatapacketspassingthroughthatvertexwheneverypairofverticessendandreceiveadatapacketalongtheshortestpathconnectingthepair.Itisfoundthattheloaddistributionfollowsapower-lawwiththeexponentδ≈2.2(1),insensitiv
3、etodifferentvaluesofγintherange,2<γ≤3,anddifferentmeandegrees,whichisvalidforbothundirectedanddirectedcases.Thus,weconjecturethattheloadexponentisauniversalquantitytocharacterizescale-freenetworks.PACSnumbers:89.70.+c,89.75.-k,05.10.-aComplexsystemsconsistofmanyconstituentssuchastheory
4、ofcriticalphenomena;however,theexponentγindividuals,substrates,andcompaniesinsocial,biolog-turnsouttobesensitivetothedetailofnetworkstruc-ical,andeconomicsystems,respectively,showingcoop-ture.Thus,auniversalquantityforSFnetworksisyettoerativephenomenabetweenconstituentsthroughdiverse
5、befound.Fromatheoreticalviewpoint,itisimportantinteractionsandadaptationstothepatterntheycreatetofindauniversalquantityforSFnetworks,whichisa[1,2].Interactionsmaybedescribedintermsofgraphs,purposeofthisLetter.consistingofverticesandedges,wherevertices(edges)AcommonfeaturebetweentheWSa
6、ndSFnetworksrepresenttheconstituents(theirinteractions).Thisap-wouldbethesmall-worldpropertythatthemeansep-proachwasinitiatedbyErd¨osandR´enyi(ER)[3].Inthearationbetweentwovertices,averagedoverallpairsofERmodel,thenumberofverticesisfixed,whileedgesvertices(calledthediameterhereafter),
7、isshorterthanconnectingonevertextoanotheroccurrandomlywiththatofaregularlattice.Thesmall-worldpropertyinSFcertainprobability.However,theERmodelistooran-networksresultsfromthepresenceofafewverticeswithdomtodescriberealcomplexsystems.Recently,Wattshighdegree.Inparticular,thehub,thevert
8、exwhosede-an
