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1、IEEECOMMUNICATIONSLETTERS1TheRich-ClubPhenomenonInTheInternetTopologyShiZhouandRa´ulJ.Mondrag´onAbstract—WeshowthattheInternettopologyattheAu-Oneofthemainpropertiesofpower–lawnetworksisthattonomousSystem(AS)levelhasarich–clubphenomenon.Theasmallnumberofnodeshavel
2、argenumbersoflinks,wecallrichnodes,whichareasmallnumberofnodeswithlargethesenodes,richnodes.InthisletterweshowthattheASnumbersoflinks,areverywellconnectedtoeachother.Thegraphshowsarich–club,i.e.acoretier.Themembersoftherich–clubisacoretierthatwemeasuredusingtheri
3、ch–clubconnectivityandthenode–nodelinkdistribution.Weobtainedclubtendtobeverywellconnectedbetweeneachother,theythiscoretierwithoutanyheuristicassumptionbetweenthecreateatightgroupwhereiftwomembersoftheclubdoASes.Therich–clubphenomenonisasimplequalitativewaynotsha
4、realink,itisverylikelythattheyshareacommontodifferentiatebetweenpowerlawtopologiesandprovidesanodethatcanlinkthem,thatistheaveragehopdistanceiscriterionfornewnetworkmodels.Toshowthis,wecomparedbetweenoneandtwo.Also,wehavecomparedtherich–clubthemeasuredrich–clubof
5、theASgraphwithnetworksobtainedusingtheBarabasi–Albert(BA)scale–freenetworkmodel,the´measuredintheASgraphwiththeoneproducedbytheBAFitnessBAmodelandtheInet–3.0model.model,theFitnessBAmodel[6]andtheInet–3.0model,wherethesyntheticnetworksarecreatedtomodeltheASIndexTe
6、rms—Internet,topology,modeling,networks.graph.OurresultsshowthattheBAandFitnessBAmodeldonotcreatearich–club.TheInet–3.0modelcreatesarich–clubI.INTRODUCTIONbutwithadeficitinthenumberofcore–links.Noticethatinthisletter,wearenottryingtocharacterizealltheexistingHEana
7、lysisoftheInternettopologyattheAutonomouspower–lawnetworkgenerators,buttoshowthatitispossibleTSystem(AS)levelbyFaloutsosetal[1]showedthattodistinguishbetweenthembystudyingthepropertiesofthetheprobabilitythatanodehasklinkshasapower–lawrich–club.tailforlargek,follo
8、wingP(k)∝k−y,y=2.22.Subra-manianetal[2],usingaheuristicargumentbasedontheII.THEASGRAPHANDITSMODELScommercialrelationshipbetweenASes,foundthattheInternetA.ASGra
