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54Vol.5No.4200812COMPLEXSYSTEMSANDCOMPLEXITYSCIENCEDec.2008:1672-3813(2008)04-0066-09,,(,200240):,:,,,,:;;;:N94;TP393.098:AEmpiricalAnalysisofanEmailNetworkinaChineseUniversityWANGKe,HUHai2bo,WANGXiao2fan(ComplexNetworksandControlLab,DepartmentofAutomation,ShanghaiJiaoTongUniversity,Shanghai200240,China)Abstract:Toexplorethecommunicationpatternofindividualsinsocialnetworks,bythelogdatawestudythestructuralpropertiesofanemailnetworkinaChineseuniversity.Twokindsofnetworksareconstructed:unmutualnetworkandmutualnetwork.Bothnetworkshaveastrongdegree2strengthcorrela2tionbutneitherofthemhasasignificantassortativeordisassortativeproperty.Moreover,wefindthatthereisarich2clubphenomenonamongthehigh2strengthnodesbutnotamongthelarge2degreenodes.Fi2nally,wedetectthecommunitystructureoftheweightedmutualnetworkbyweightedfitnessalgorithmandfindthatthecumulativedistributionofcommunitysizefollowspowerlaw.Theresultsprovideempiri2calfoundationformodel2buildingandsimulations.Keywords:e2mailnetwork;weightednetwork;smallworld;rich2club:2008-10-06:(70431002);(60674045,60731160629);(07XD14017):(1985-),,,,1,[1],[2-8][9-10]MSN[11],[12-13],Internet,54,:,,[3],[5]()[5],,[4],Barabsi[7-8],2006820078378,,:,,,,,2378,20068192007831,,,,googlehotmail,,,,40032,3674315,911781a,,,,200,,,1b,,,,,1,Ebel,[3];Guimer50,[5];Tsaiw,wij=wjiij[4]76200812,,,,,:,:,,ij,ji,39141,97177%,29953,99198%20169,50138%,124705,99195%,,,,,,,,,1,,,,,1000,,120169391411247052995530.0006130.0003914.792.951290.20050.201633.1,EbelKiel-1181[3],GuimerRoviraiVir2gili[5][14],228654,:2167e-1.06x0.32,,1000,Kmax=19184,2000,,,135,,15,15,,,2119e-0.76x0.41,,,2b,,200,,150[15],,,,3.2,1000,,100,,si=6jN(vi)wij,wijij3-3,2127e-0.74x0.3733,,,3.3,,,,-,-Pearson[16],:96200812r=M-16ijiki-M-16i12(ji+ki)2M-16i12(j2i+k2i)-M-16i12(ji+ki)2(1),ji,kii(i=1,,M,M),-1r1r,,;,r0,-,22--0.00290.0777-0.0603-0.11872,,,,,,,,1000,,,,,,,,,()(),,,4k,s(k),:s(k)k(2)11591127,[17],,43.4,,,0754,:,ci=2Eiki(ki-1)(3)Eii,kii[17]cwi=1si(ki-1)6j,hN(vi)(wij+wjh)2ajh(4)sii,kii,aijij,1,0,wijij,012,0112,5c(k),k,k,,5,100,,100,,,BoguÌTsai[4,18]544.1[19],,(),,:(k)=2EkNk(Nk-1)(5),Nkk,EkZho[20],(k)k,Colizza[21],ER,MRBA(k)k,(k)rand(k),(k)=(k)/rand(k)(6)1,JiangColizza17200812[22],N,N(k)=(k)/rand(k),k,p=#[^(g)1]n(7)p,,p0105,650,gk66a,kk,6b6c,,,,,,(),6,34.2,,,,w(k)=2EwNw(Nw-1)(8),Nww,Ew(6)(7),7,,7,32754,:,,,,3,,5,N(I)I-,,I,[23],,[24],fG=kGin(kGin+kGout)(9),kGinkGoutG,,=18,-017475RoviraIVirgiliarxiv,-0148-1107[23]86,,,,,,,,,,,,,,:[1]WattsDJ.Atwenty2firstcenturyscience[J].Nature,2007,445:489.[2]KossinetsG,WattsDJ.Empiricalanalysisofanevolvingsocialnetwork[J].Science,2006,311:88-90.[3]EbelH,MielschLI,BornholdtS.Scale2freetopologyofe2mailnetworks[J].PhysRevE,2002,66:035103.[4]TsaiY,LinCC,LinCC.Characteristicsofweightedemailcommunications[C].TheFifthInternationalConferenceonInfor2mation,CommunicationsandSignalProcessing.Bangkok,Thailand,2005:399-403.[5]GuimerR,DanonL,Daz2GuileraA,etal.Self2similarcommunitystructureinanetworkofhumaninteractions[J].PhysRevE,2003,68:065103(R).37200812[6]EckmannJP,MosesE,SergiD.Entropyofdialoguescreatescoherentstructuresine2mailtraffic[J].ProcNatlAcadSciUSA,2004,101:14333-14337.[7]VzquezA,OliveiraJG,DezsÊZ,etal.Modelingburstsandheavytailsinhumandynamics[J].PhysRevE,2006,73:036127.[8]BarabsiAL.Theoriginofburstsandheavytailsinhumandynamics[J].Nature,2005,435:207-211.[9]OnnelaJP,Saram¾kiJ,HyvÊnenJ,etal.Structureandtiestrengthsinmobilecommunicationnetworks[J].ProcNatlAcadSciUSA,2007,104:7332-7336.[10]OnnelaJP,Saram¾kiJ,HyvÊnenJ,etal.Analysisofalarge2scaleweightednetworkofone2to2onehumancommunication[J].NewJournalofPhysics,2007,9:179.[11]LeskovecJ,HorvitzE.Planetary2scaleviewsonalargeinstant2messagingnetwork[C]//Proceedingofthe17thinternationalconferenceonWorldWideWeb.NewYork:ACMPress,2008:915-924.[12]HolmeP,EdlingCR,LiljerosF.Structureandtimeevolutionofaninternetdatingcommunity[J].SocialNetworks,2004,26:155-174.[13],,,.[J].,2008,5(2):1-14.HuHaibo,WangKe,XuLing,etal.Analysisofonlinesocialnetworksbasedoncomplexnetworktheory[J].ComplexSystemandComplexScience,2008,5(2):1-14.[14]LaherrreJ,SornetteD.Stretchedexponentialdistributionsinnatureandeconomy:fattailswithcharacteristicscales[J].EurPhysJB,1998,2:525-539.[15]DunbarRIM.Coevolutionofneocorticalsize,groupsizeandlanguageinhumans[J].BehavioralandBrainSciences,1993,16(4):681-735.[16]FuF,ChenX,LiuL,etal.Socialdilemmasinanonlinesocialnetwork:thestructureandevolutionofcooperation[DB/OL].[2007-12-01].[17]BarratA,BarthlemyM,Pastor2SatorrasR,etal.Thearchitectureofcomplexweightednetworks[J].ProcNatlAcadSciUSA,2004,101:3747-3752.[18]BoguÌM,Pastor2SatorrasR,Daz2GuileraA,etal.Modelsofsocialnetworksbasedonsocialdistanceattachment[J].PhysRevE,2004,70:056122.[19]ZhouS,MondragnRJ.Accuratelymodelingtheinternettopology[J].PhysRevE,2004,70:066108.[20]ZhouS,MondragnRJ.Therich2clubphenomenonintheinternettopology[J].IEEECommunLett,2004,8:180-182.[21]ColizzaV,FlamminiA,SerranoMA,etal.Detectingrich2cluborderingincomplexnetworks[J].NatureP