Box-Covering Fractal Dimension of Complex Network: From the View of Effective Distance

Abstract

The fractal property of networks, that is, self-similarity, is a basic but important topic in the area of complex networks. In the process of studying the fractal characteristics of complex networks, the topological distance of unweighted networks is often used to represent the network. However, this ignores some local information of the network, such as the contribution of edges to node degrees. It is inconsistent with common sense. Therefore, in this paper, we propose a new algorithm which replace the traditional topological distance with the effective distance to calculate fractal dimension reasonably. Moreover, we apply this algorithm to five real networks, and the experiment results show the effectiveness and correctness of using effective distance instead of topological distance.