论文《交通流驱动的含权网络》

http:PP­(230026),.,,.,,,,,AweightedcomplexnetworkmodeldrivenbytrafficflowWANGBing2Hong­WANGWen2XuZHOUTao(DepartmentofModernPhysics,UniversityofScienceandTechnologyofChina,Hefei230026,China)AbstractWereviewrecentprogressintheresearchonweightedcomplexnetworks.Inparticular,wepres2entourrecentmodelofatrafficflowdrivenweightedtechnologicalnetwork.Thismodelcanshowsimultaneous2lyfivecharacteristicsofarealnetworksuchasthepowerlawdistributionforthedegreeofconnection,strength,weighting,aswellasthelargeclusteringcoefficientandnon2assortativemixingproperty.Hence,thismodelde2scribessuccessfullyscale2freebehaviorandsmall2worldeffectsofrealtechnologicalcomplexnetworks.Keywordsweightednetworks,drivenbytrafficflow,technologicalnetwork,smallworldeffect,sale2freenetwork,powerlaw3(:10472116,70271070,10532060,10547004)(SRFDP20020358009)2005-07-28,2005-09-26­.Email:[e-mail]1,(Inter2net)[1](worldwideweb)[2][3,4][5,6].,,.,.[7,8].,,.1.[8].1WSBA:40335(2006)4http:PP(WS),,[9].1999,BarabsiAlbert[10].:.(BA).WSBA.WSBA..Dorogovtsev-Mendes-Samukin[11],BA,.,KlemmEguiluz[12],,,.Holme-Kim[13],BA,,.Szabo[14].,[1518]..,Newman,[19],,.RavaszBarabsi,[20].(),.,Amaral,,[21].KlemmEguiluz[12].,[22],[23],[24].,,.?..,[4].,.,..,;;,.,,.,,.Barrat-Barthelemy-Vespignani(BBV)[6,25].,power-law,.,23.[26].BBV,,.,,,(assortative),(disassortative)[19]..(),,.[27]503http:PP=1,,N,N,.,wijij,.,:wij=wji.(kP(k))[5,6]:P(k)k-,(1)23.(w)P(w).P(w),,[28].:si=j(i)wi,j,(2)i(i).,.,,.,P(s).:,[29,30]:sk.(3)d=1N(N-1)ijdij,(4)dijij.C=1Nici,(5)ci=1ki(ki-1)j,hai,jai,haj,h(6)i.ai,j:ai,j=1,ij;0,ij(assortativemixing):,.,.(assortativemix2ing)[31].(disassorta2tive),.Newman(assortativecoeffi2cient)r.,:,,.??.2.[31]:r=M-1ijiki-12M-1i(ji+Ki)212M-1i[(ji)2+(ki)2]-12M-1i(ji+ki)2,(10):i=1,,M,M.,jii(),kii().,:ji=ji-1..,,.3,60335(2006)4http:PP:,n,m,:BAni=kijkj=knkijknkj.(11),BBV,nini=sijsj=snsijsnsj.(12):,,.:,,.:.,Dorogovtsev-Mendes2000,,[32]..():,(),..,,.,..N0,w0():,m,(12),.w0=1.():,():wijwij+1,Wpij,wij,1-Wpij,(13)pij=sisjabsasb(14)ij(),wij.ij,wij=0.ijwij=W(15),,.,W.,,W..N0,(13)Wpij1,,1.,,.,..4,:t=N-N0.,N.,,.W.703http:PP[1,33].,(13)dwijdt=2Wsisja,b(ab)sasb=2Wsisjasab(a)sb.(16)isi,i(),i()().:dsidt=j(i)2Wsisjasab(a)sb+msilsl.(17)isi(t)2(m+W)t,dsidt=2W+m2W+2msit.(18)[25,33]:P(s)s-,=2+m/(m+2W).,W=0,BA,=3.W,,W,2.5N0=3,m=3W0=1,W.,..1P(s)ssk,.BBV=1,,W[1(b)],.,-DM[32].DM,,.sk,,,.,skP(s)s-,:P(k)k-,.P(k)dk=P(s)ds,=(-1)+1.1(a)P(s),s.,,=2+m/(m+2W).N=500020;(b)W,siki().W=1,5,10,15,1.04,1.17,1.25,1.30,:sk2..2(a)P(k)k-;(b)P(w)w-.N=5000203Cr.,BA,,.,CW,W,C1,80335(2006)4http:PP(a)CW.C(CN),’(b)rW.r,6.(W),,(k)(s)(w),,CrW.,.,..,,.,,[34]?.,...,.[27],1,2,3,[1]Pastor-SatorrasR,VespignaniA.EvolutionandStructureoftheInternet:AStatisticalPhysicsApproach.Cambridge:Cam2bridgeUniversityPress,2004[2]AlbertR,JeongH,BarabasiA2L.Nature,1999,401:130[3]NewmanMEJ.Phys.Rev.E,2001,64:016132[4]BarabasiA2L,JeongH,NedaZetal.PhysicaA,2002,311:590[5]GuimeraR,MossaS,TurtschiAetal.cond2mat/0312535[6]BarratA,BarthelemyM,Pastor2SatorrasRetal.Proc.Natl.Acad.Sci.U.S.A.,2004,101:3747[7],,.,2005,15(5):513[ZhouT,FuZQ,NiuYWetal.ProgressinNaturalSci2ence,2005,15(5):513(inChinese)][8],,.,2005,34(1):31[ZhouT,BaiWJ,WangBHetal.Wuli(Physics),2005,34(1):31(inChinese)][9]WattsDJ,StrogatzSH.Nature,1998,393:440[10]BarabsiA2L,AlbertR.Science,1999,286:509[11]DorogovtsevSN,MendesJFF,SamukinAN.Phys.Rev.E,2001,63:062101[12]KlemmK,EguiluzVM.Phys.Rev.E,2002,65:057102[13]HolmeP,KimBJ.Phys.Rev.E,2002,65:026107[14]SzaboG,AlavaM,KerteszJ.Phys.Rev.E,2003,67:056102[15]AndradeJr.JS,HerrmannHJ,AndradeRFSetal.Phys.Rev.Lett.,2005,94:018702[16]DoyeJPK,MassenCP.Phys.RevE,2005,71:016128[17]ZhouT,YanG,WangBH.Phys.Rev.E,2005,71:046141[18]ZhouT,YanG,ZhouP2L,etal.arXiv:cond2mat/0409414903http:PP[19]NewmanMEJ.Phys.Rev.Lett.,2002,89:208701[20]RavaszE,BarabsiA2L.Phys.Rev.E,2003,67:026112[21]AmaralLAN,ScalaA,BarthelemyMetal.PNAS,2000,97:11149[22]DorogovtsevSN,MendesJFF.Phys.Rev.E,2000,62:1842[23]ZhuH,WangX2R,ZhuJ2Y.Phys.Rev.E,2003,68:056121[24]JiangP2Q,WangB2H,ZhouT.Chin.Phys.Lett.,2005,22(5):1285[25]BarratA,BarthlemyM,VespignaniA.Phys.Rev.Lett.,2004,92:228701[26]NewmanMEJ.SIAMReview,2003,45:167[27]WangW2X,WangB2H,HuBetal.Phys.Rev.Lett.,2005,94:188702[28]LiW,CaiX.Phys.Rev.E,2004,69:046106[29]GohK2I,KahngB,KimD.cond2mat/0410078[30]Pastor2SatorrasR,VazquezA,VespignaniA.condmat/0105161[31]NewmanMEJ.Phys.Rev.E,2003,67:026126[32]DorogovtsevSN,MendesJFF.Europhys.Lett.,2000,52:33[33]AlbertR,BarabasiA2L.Rev.Mod.Phys.,2002,74:47[34]CaldarelliG,ErzanA,VespignaniA.Eur.Phys.J.B,2004,38:143()(,),59.00200512O-236368.0020051259.00200512O-234768.0020056O-214837.0020055O-214732.0020053O-1900120.0020055O-209338.0020051O-2016,50.0020051O-200448.0020051O-1830(),98.0020053O-197658.0020052O-195245.0020048O-1802,42.0020048O-2027,56.0020047O-1942X59.0020039O-1682()99.002003548.0020035O-130142.0020033O-154215.002