Multifractal analysis of weighted networks by a modified sandbox algorithm

TL;DR

This paper introduces a modified sandbox algorithm for multifractal analysis of weighted networks, demonstrating its effectiveness on theoretical fractal networks and real-world collaboration networks, revealing multifractality influenced by edge weights.

Contribution

A novel modified sandbox algorithm (SBw) for multifractal analysis of weighted networks, validated on theoretical models and real-world data.

Findings

SBw algorithm accurately characterizes multifractality in weighted networks.

Fractal dimensions vary with edge weights in weighted fractal networks.

Multifractality is present in real weighted collaboration networks, affected by edge weights.

Abstract

Complex networks have attracted growing attention in many fields. As a generalization of fractal analysis, multifractal analysis (MFA) is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. Some algorithms for MFA of unweighted complex networks have been proposed in the past a few years, including the sandbox (SB) algorithm recently employed by our group. In this paper, a modified SB algorithm (we call it SBw algorithm) is proposed for MFA of weighted networks.First, we use the SBw algorithm to study the multifractal property of two families of weighted fractal networks (WFNs): "Sierpinski" WFNs and "Cantor dust" WFNs. We also discuss how the fractal dimension and generalized fractal dimensions change with the edge-weights of the WFN. From the comparison between the theoretical and numerical fractal dimensions of these networks, we can find that the proposed SBw algorithm is efficient and feasible for MFA of weighted networks. Then, we apply the SBw algorithm to study multifractal properties of some real weighted networks ---collaboration networks. It is found that the multifractality exists in these weighted networks, and is affected by their edge-weights.