A novel scale-free network model based on clique growth

Abstract

A novel scale-free network model based on clique (complete subgraph of random size) growth and preferential attachment was proposed. The simulations of this model were carried out. And the necessity of two evolving mechanisms of the model was verified. According to the mean-field theory, the degree distribution of this model was analyzed and computed. The degree distribution function of vertices of the generating network P(d) is 2m²m₁⁻³ (d − m₁ + 1)⁻³, where m and m₁ denote the number of the new adding edges and the vertex number of the cliques respectively, d is the degree of the vertex, while one of cliques P(k) is 2m²k⁻³, where k is the degree of the clique. The simulated and analytical results show that both the degree distributions of vertices and cliques follow the scale-free power-law distribution. The scale-free property of this model disappears in the absence of any one of the evolving mechanisms. Moreover, the randomicity of this model increases with the increment of the vertex number of the cliques.

Keywords

scale-free / clique growth / preferential attachment / degree distribution

References

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

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

[3] DorogovtsevS. N., MendesJ. F. F., SamukhinA. N.. Structure of growing networks with preferential linking [J]. Physical Review Letters, 2000, 85(21): 4633-4636

[4] KRAPIVSKY P L, REDNER S. Organization of growing random networks [J]. Physical Review E, 2001, 63(6): 066123.

[5] KrapivskyP. L., RednerS., LeyvrazF.. Connectivity of growing random networks [J]. Physical Review Letters, 2000, 85(21): 4629-4632

[6] BianconiG., BarabasiA. L.. Bose-Einstein condensation in complex networks [J]. Physical Review Letters, 2001, 86(24): 5632-5635

[7] LiX., ChenG.. A local world evolving network model [J]. Physica A, 2003, 328(1/2): 274-286

[8] MiloR., Shen-OrrS., ItzkovitzS., KashtanN., ChklovskiiD., AlonU.. Network motifs: Simple building blocks of complex networks [J]. Science, 2002, 298(5594): 824-827

[9] ShiffrinR. M., BornerK.. Mapping knowledge domains [J]. Proc Natl Acad Sci, 2004, 101(1): 5183-5185

[10] EverittB. S.Cluster analysis [M], 1993, London, Edward Arnold

[11] KnudsenS.A guide to analysis of DNA microarray data [M], 2004, New York, Wiley-Liss

[12] NewmanM. E. J.. Detecting community structure in networks [J]. The European Physical Journal B, 2004, 38(2): 321-330

[13] ChenA.-b., CaiZ.-x., HuD.-wen.. Clustering in mobile ad hoc network based on neural network [J]. Journal of Central South University of Technology, 2006, 13(6): 699-702

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

[15] AdamcsekB., PallaG., FarkasI. J., VicsekT.. CFinder: Locating cliques and overlapping modules in biological networks [J]. Bioinformatics, 2006, 22(8): 1021-1023

[16] DERENYII, PALLAG, VICSEKT. Clique percolation in random networks [J]. Physical Review Letters, 2005, 94(16): 160202

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

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