On Power-Law Relationships of the Internet Topology.pdf

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1、OnPower-LawRelationshipsoftheInternetTopologyMichalisFaloutsosPetrosFaloutsosChristosFaloutsos*U.C.RiversideU.ofTorontoCarnegieMellonUniv.Dept.ofComp.ScienceDept.ofComp.ScienceDept.ofComp.Sciencemichalis@cs.ucr.edupfal@cs.toronto.educhristosQcs.cmu.eduAbstracthops)that

2、areusefulfortheanalysisofprotocolsandforspeculationsoftheInternettopologinthefuture.DespitetheapparentrandomnessoftheInternet,wedis-ModelingtheInternettopologyP.isanimportantopencoversomesurprisinglysimplepower-lawsoftheInternetproblemdespitetheattentionithasattractedr

3、ecently.Pax-topology.Thesepower-lawsholdforthreesnapshotsofthesonandFloydconsiderthisproblemasamajorreason“WhyInternet,betweenNovember1997andDecember1998,de-WeDon’tKnowHowToSimulateTheInternet”[16].Sev-spitea45%growthofitssizeduringthatperiod.Weshoweralgraph-generatorm

4、odelshavebeenproposed[23][5][27],thatourpower-lawsfittherealdataverywellresultinginbuttheproblemofcreatingrealistictopologiesisnotyetcorrelationcoefficientsof96%orhigher.solved;theselectionofseveralparametervaluesarelefttoOurobservationsprovideanovelperspectiveofthestr

5、uc-theintuitionandtheexperienceofeachresearcher.tureoftheInternet.Thepower-lawsdescribeconciselyAsourprimarycontribution,weidentifythreepower-skeweddistributionsofgraphpropertiessuchasthenodelawsforthetopologyoftheInternetoverthedurationofaoutdegree.Inaddition,thesepow

6、er-lawscanbeusedtoyearin1998.Power-lawsareexpressionsoftheformy0:zQ,estimateimportantparameterssuchastheaverageneigh-whereaisaconstant,zandyarethemeasuresofinterest,borhoodsize,andfacilitatethedesignandtheperformanceando(standsfor“proportionalto”.Someofthoseexponentsan

7、alysisofprotocols.Furthermore,wecanusethemtogen-donotchangesignificantlyovertime,whilesomeexponentserateandselectrealistictopologiesforsimulationpurposes.changebyapproximately10%.However,theimportantob-servationistheexistenceofpower-laws,i.e.,thefactthat1Introductionth

8、ereissomeexponentforeachgraphinstance.During1998,thesepower-lawsholdinthreeInternetinstanceswith“WhatdoestheInternetl