Sandbox edge-based algorithm for multifractal analysis of complex networks

Abstract

Multifractal analysis of complex networks has attracted increasing interest in various fields of science, because it can help us unfold the intricate structure of a variety of networks for better understanding the underlying mechanism of these networks. In this study, we propose a sandbox edge-based (SBEB) multifractal analysis algorithm, which introduces the idea of the sandbox algorithm into the existing edge-based box-counting (EBBC) algorithm. Instead of using boxes to cover the nodes of a given network, the SBEB algorithm uses boxes to cover the entries ‘1’ in the adjacency matrix of the network, where these entries ‘1’ represent the edges of the network. We apply the SBEB algorithm to model networks to verify its effectiveness and feasibility. The results show that the SBEB algorithm can effectively capture the multifractal nature of these model networks. Compared with the existing EBBC algorithm, our algorithm greatly improves the linearity and smoothness in estimating the mass exponents τ(q) and the generalized fractal dimensions D(q), thereby resulting in more accurate estimates. In addition, the SBEB algorithm inherits the advantage of the existing EBBC algorithm on studying small-diameter networks which are difficult to be dealt with by the traditional node-based box-covering algorithms. In application, we apply the SBEB algorithm to several real-world networks, and results indicate that this algorithm can uncover their genuine multifractal behaviors.