FRACTAL NETWORKS on SIERPINSKI-TYPE POLYGON

In this paper, the evolving networks are created from a series of Sierpinski-type polygon by applying the encoding method in fractal and symbolic dynamical system. Based on the self-similar structures of our networks, we study the cumulative degree distribution, the clustering coefficient and the standardized average path length. The power-law exponent of the cumulative degree distribution is deduced to be log2n and the average clustering coefficients have a uniform lower bound 2n-3 3n. Moreover, we find the asymptotic formula of the average path length of our proposed networks. These results show the scale-free and the small-world effects of these networks.