THE SCALE-FREE AND SMALL-WORLD PROPERTIES OF COMPLEX NETWORKS ON SIERPINSKI-TYPE HEXAGON

摘要

In this paper, a network is generated from a Sierpinski-type hexagon by applying the encoding method in fractal. The criterion of neighbor is established to quantify the relationships among the nodes in the network. Based on the self-similar structures, we verify the scale-free and small-world effects. The power-law exponent on degree distribution is derived to be log(2) 6 and the average clustering coefficients are shown to be larger than 0.4255. Moreover, we give the bounds of the average path length of our proposed network from the renewal theorem and self-similarity.