Multi-fractal analysis of weighted networks

TL;DR

This paper introduces a novel multifractal analysis method for weighted networks using a box-covering algorithm, enabling a more comprehensive understanding of their fractal properties.

Contribution

It proposes a new multifractal dimension calculation method for weighted networks, extending fractal analysis beyond unweighted networks.

Findings

The method effectively calculates fractal dimensions of real weighted networks.

Numerical results demonstrate the efficiency of the proposed multifractal analysis.

The approach provides deeper insights into the fractal properties of complex weighted networks.

Abstract

In many real complex networks, the fractal and self-similarity properties have been found. The fractal dimension is a useful method to describe fractal property of complex networks. Fractal analysis is inadequate if only taking one fractal dimension to study complex networks. In this case, multifractal analysis of complex networks are concerned. However, multifractal dimension of weighted networks are less involved. In this paper, multifractal dimension of weighted networks is proposed based on box-covering algorithm for fractal dimension of weighted networks (BCANw). The proposed method is applied to calculate the fractal dimensions of some real networks. Our numerical results indicate that the proposed method is efficient for analysis fractal property of weighted networks.