Multifractal Analysis of Weighted Complex Networks Based on Degree Volume Dimension

Abstract

In the research field of complex networks, the network nodes and edges are the fundamental indicators and often used as the preliminary step in the structural analysis of complex networks. In this paper, first, considering the differences in the node degree distribution, the traditional box-covering algorithm is modified by regarding the number of nodes in the box as the node degree, it is proved that multifractal characteristics are the nature of weighted complex networks. Moreover, multifractal spectrums of eight different networks are obtained and the variations in three eigenvalues corresponding are further analyzed, by comparing the existing and modified algorithms. Finally, we can make the practical conclusion that the multifractal characteristics of weighted complex networks are affected by the differences in the node degree distribution.INDEX TERMS Degree volume dimension, multifractal, modified box-covering algorithm, weighted complex networks.