A novel weighted evolving network model based on clique overlapping growth

Abstract

A novel weighted evolving network model based on the clique overlapping growth was proposed. The model shows different network characteristics under two different selection mechanisms that are preferential selection and random selection. On the basis of mean-field theory, this model under the two different selection mechanisms was analyzed. The analytic equations of distributions of the number of cliques that a vertex joins and the vertex strength of the model were given. It is proved that both distributions follow the scale-free power-law distribution in preferential selection mechanism and the exponential distribution in random selection mechanism, respectively. The analytic expressions of exponents of corresponding distributions were obtained. The agreement between the simulations and analytical results indicates the validity of the theoretical analysis. Finally, three real transport bus networks (BTNs) of Beijing, Shanghai and Hangzhou in China were studied. By analyzing their network properties, it is discovered that these real BTNs belong to a kind of weighted evolving network model with clique overlapping growth and random selection mechanism that was proposed in this context.

Keywords

weighted network / clique overlapping / mean-field theory / bus transport network

References

[1] AlbertR., BarabasiA. L.. Statistical mechanics of complex networks [J]. Review of Modern Physics, 2002, 74(1): 47-97

[2] NewmanM. E. J.. The structure and function of complex networks [J]. SIAM Review, 2003, 45(2): 167-256

[3] ZhouT., BaiW.-j., WangB.-h., LiuZ.-j., YanGang.. A brief review of complex networks [J]. Physics, 2005, 34(1): 31-36

[4] WattsD. J., StrogatzS. H.. Collective dynamics of ’small-world’ networks [J]. Nature, 1998, 393(6684): 440-442

[5] BarabasiA. L., AlbertR.. Emergence of scaling in random networks [J]. Science, 1999, 286(5439): 509-512

[6] PallaG., DerenyiI., FarkasI., VicsekT.. Uncovering the overlapping community structure of complex networks in nature and society [J]. Nature, 2005, 435(7043): 814-818

[7] DerenyiI., PallaG., VicsekT.. Clique percolation in random networks [J]. Physical Review Letters, 2005, 94(16): 160202

[8] CardilloA., ScellatoS., LatoraV.. A topologic analysis of scientific coauthor ship networks [J]. Physica A, 2006, 372(2): 333-339

[9] TomassiniM., LuthiL.. Empirical analysis of the evolution of a scientific collaboration network [J]. Physica A, 2007, 385(2): 750-764

[10] HeN., GanW.-y., LiD.-y., KangJ.-chu.. The topological analysis of a small actor collaboration network [J]. Complex Systems and Complexity Science, 2006, 3(4): 1-10

[11] LiuA.-f., FuC.-h., ZhangZ.-p., ChangH., HeD.-ren.. An empirical statistical investigation on Chinese mainland movie network [J]. Complex Systems and Complexity Science, 2007, 4(3): 10-17

[12] HeY., ZhangP.-p., TangJ.-y., HanX.-f., QiuR., ChenQ.-j., ZhouY.-p., ChangH., HeD.-ren.. A collaboration network description on traditional Chinese medical prescription formulation system [J]. Science and Technology Review, 2005, 23(11): 36-39

[13] ChangH., SuB.-b., ZhouY.-p., HeD.-ren.. Assortativity and act degree distribution of some collaboration networks [J]. Physica A, 2007, 383(2): 687-702

[14] YangX.-h., WangB., WangW.-l., SunY.-xian.. Research on some bus transport networks with random overlapping clique structure [J]. Communications in Theoretical Physics, 2008, 50(5): 1249-1254

[15] GuimeraR., UzziB., SpiroJ., AmaralL. A. N.. Team assembly mechanisms determine collaboration network structure and team performance [J]. Science, 2005, 308(7722): 697-702

[16] RamascoJ. J., DorogovtsevS. N., Pastor-satorrasR.. Self-organization of collaboration networks [J]. Physical Review E, 2004, 70(3): 036106

[17] ZhouT., WangB.-h., JinY.-d., HeD.-r., ZhangP.-p., HeY., SuB.-b., ChenK., ZhangZ.-z., LiuJ.-guo.. Modelling collaboration networks based on nonlinear preferential selection [J]. International Journal of Modern Physics C, 2007, 18(2): 297-314

[18] ZhangP.-p., ChenK., HeY., ZhouT., SuB.-b., JinY.-d., ChangH., ZhouY.-p., SunL.-c., WangB.-h., HeD.-ren.. Model and empirical study on some collaboration networks [J]. Physica A, 2006, 360(2): 599-616

[19] ChenY.-z., LiN., HeD.-ren.. A study on some urban bus transport networks [J]. Physica A, 2007, 376: 747-754

[20] WangW.-x., WangB.-h., HuB., YanG., OuQing.. General dynamics of topology and traffic on weighted technological networks [J]. Physical Review Letter, 2005, 94(18): 188702

[21] BarratA., BarthelemyM., VespignaniA.. Weighted evolving networks: Coupling topology and weight dynamics [J]. Physical Review Letters, 2004, 92(22): 228701

[22] BraunsteinL., WuZ., ChenY., BuldyrenS., SreenivasanS., KaliskyT., CohenR., LopezE., HavlinS., StanleyHe.. Optimal path and minimal spanning trees in random weighted networks [J]. International Journal of Bifurcation and Chaos, 2007, 17(7): 2215-2255

[23] BarabasiA. L., AlbertR., JeongH.. Mean-field theory for scale-free random networks [J]. Physica A, 1999, 272(1/2): 173-187