Unveiling the Multi-fractal Structure of Complex Networks

TL;DR

This paper introduces a new edge-focused method to analyze the fractal structures of complex networks, distinguishing between mono-fractal, quasi mono-fractal, and multi-fractal behaviors efficiently.

Contribution

It presents a practical, computationally efficient approach for revealing fractal properties of networks based on edges, emphasizing the role of degree homogeneity.

Findings

Degree homogeneity influences fractal nature of networks.

Analysis of protein-protein interaction networks reveals varying complexity levels.

Method effectively distinguishes different fractal structures.

Abstract

The fractal nature of graphs has traditionally been investigated by using the nodes of networks as the basic units. Here, instead, we propose to concentrate on the graph edges, and introduce a practical and computationally not demanding method for revealing changes in the fractal behavior of networks, and particularly for allowing distinction between mono-fractal, quasi mono-fractal, and multi-fractal structures. We show that degree homogeneity plays a crucial role in determining the fractal nature of the underlying network, and report on six different protein-protein interaction networks along with their corresponding random networks. Our analysis allows to identify varying levels of complexity in the species.