A unified model for Sierpinski networks with scale-free scaling and small-world effect

作者：Guan Jihong; Wu Yuewen; Zhang Z*******^*; Zhou Shuigeng; Wu Yonghui

来源：Physica A: Statistical Mechanics and Its Applications , 2009, 388(12): 2571-2578.

DOI：10.1016/j.physa.2009.03.005

• Complex networks
• Scale-free networks
• Fractals

In this paper, we propose ail evolving Sierpinski gasket, based on which we establish a model of evolutionary Sierpinski networks (ESNs) that unifies deterministic Sierpinski network [Z.Z. Zhang, S.G. Zhou, T. Zoo, L.C. Chen, J.H. Guan, Eur. Phys. J. B 60 (2007) 259] and random Sierpinski network [Z.Z. Zhang, S.G. Zhou, Z. Su, T. Zou, J.H. Guan, Eur. Phys. J. B 65 (2008) 141] to the same framework. We suggest ail iterative algorithm generating the ESNs. Oil the basis of the algorithm, some relevant properties of presented networks are calculated or predicted analytically. Analytical Solution shows that the networks under consideration follow a power-law degree distribution, with the distribution exponent continuously tuned in a wide range. The obtained accurate expression of Clustering coefficient, together with the prediction of average path length reveals that the ESNs possess small-world effect. All our theoretical results are Successfully contrasted by numerical simulations. Moreover, the evolutionary prisoner';s dilemma game is also studied on some limitations of the ESNs, i.e., deterministic Sierpinski network and random Sierpinski network.

• 出版日期2009-6-15
• 单位复旦大学