Self-affine Fractals Embedded in Spectra of Complex Networks

TL;DR

This paper investigates the multifractal nature of spectra in real-world complex networks using wavelet transforms, revealing classification based on long-range correlation exponents linked to hierarchical structures.

Contribution

It introduces a novel analysis of complex network spectra, demonstrating their multifractal properties and classifying networks by the Hust exponent, highlighting hierarchical features.

Findings

Spectra of real-world networks are multifractal.

Networks are classified into three types based on the Hust exponent.

All considered networks have $H \,\geq\, 0.5$, indicating hierarchical properties.

Abstract

The scaling properties of spectra of real world complex networks are studied by using the wavelet transform. It is found that the spectra of networks are multifractal. According to the values of the long-range correlation exponent, the Hust exponent $H$, the networks can be classified into three types, namely, $H>0.5$, $H=0.5$ and $H<0.5$. All real world networks considered belong to the class of $H \ge 0.5$, which may be explained by the hierarchical properties.