An extended clique degree distribution and its heterogeneity in cooperation–competition networks

Ai-Xia Feng, Chun-Hua Fu, Xiu-Lian Xu, Yue-Ping Zhou, Hui Chang, Jian Wang, Da-Ren He and Guo-Lin Feng

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 7, 2454-2462

Abstract: After Xiao et al. [W.-K. Xiao, J. Ren, F. Qi, Z.W. Song, M.X. Zhu, H.F. Yang, H.Y. Jin, B.-H. Wang, Tao Zhou, Empirical study on clique-degree distribution of networks, Phys. Rev. E 76 (2007) 037102], in this article we present an investigation on so-called k-cliques, which are defined as complete subgraphs of k (k>1) nodes, in the cooperation–competition networks described by bipartite graphs. In the networks, the nodes named actors are taking part in events, organizations or activities, named acts. We mainly examine a property of a k-clique called “k-clique act degree”, q, defined as the number of acts, in which the k-clique takes part. Our analytic treatment on a cooperation–competition network evolution model demonstrates that the distribution of k-clique act degrees obeys Mandelbrot distribution, P(q)∝(q+α)−γ. To validate the analytical model, we have further studied 13 different empirical cooperation–competition networks with the clique numbers k=2 and k=3. Empirical investigation results show an agreement with the analytic derivations. We propose a new “heterogeneity index”, H, to describe the heterogeneous degree distributions of k-clique and heuristically derive the correlation between H and α and γ. We argue that the cliques, which take part in the largest number of acts, are the most important subgraphs, which can provide a new criterion to distinguish important cliques in the real world networks.

Keywords: Cooperation–competition; k-clique; Heterogeneity (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:7:p:2454-2462

DOI: 10.1016/j.physa.2011.12.013

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