Abstract This paper studies a simple asymmetrically evolved community network with a combination of preferential attachment and random properties. An important issue about community networks is to discover the different utility increments of two nodes, where the utility is introduced to investigate the asymmetrical effect of connecting two nodes. On the other hand, the connection of two nodes in community networks can be classified as two nodes belonging to the same or to different communities. The simulation results show that the model can reproduce a power-law utility distribution P(u)～u-σ, σ = 2 + 1/p, which can be obtained by using mean-field approximation methods. Furthermore, the model exhibits exponential behaviour with respect to small values of a parameter denoting the random effect in our model at the low-utility region and a power-law feature with respect to big values of this parameter at the high-utility region, which is in good agreement with theoretical analysis. This kind of community network can reproduce a unique utility distribution by theoretical and numerical analysis.
Received: 27 March 2008
Revised: 17 July 2008
Accepted manuscript online:
(Fluctuation phenomena, random processes, noise, and Brownian motion)
Fund: Project
supported by National Basic Research Program of China (Grant No
2006CB705500), Chang-jiang Scholars and Innovative Research Team in
University (Grant No IRT0605), National Natural Science Foundation
of China (Grant No 70631001).
Cite this article:
Cui Di(崔迪), Gao Zi-You(高自友), and Zheng Jian-Feng(郑建风) Properties of asymmetrically evolved community networks 2009 Chin. Phys. B 18 516
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