Fractal dimensions of complex networks: advocating for a topological approach

TL;DR

This paper advocates for applying Topological Data Analysis to estimate fractal dimensions of complex networks, highlighting potential advantages and discussing challenges in integrating topological methods with network analysis.

Contribution

It introduces the idea of using TDA for fractal dimension estimation in networks, proposing a topological approach as a novel perspective.

Findings

TDA methods outperform existing techniques in estimating fractal dimensions.

Higher-order interactions are crucial for understanding complex network structures.

The paper outlines challenges and potential benefits of topological approaches in network analysis.

Abstract

Topological Data Analysis (TDA) uses insights from topology to create representations of data able to capture global and local geometric and topological properties. Its methods have successfully been used to develop estimations of fractal dimensions for metric spaces that have been shown to outperform existing techniques. In a parallel line of work, networks are ubiquitously used to model a variety of complex systems. Higher-order interactions, i.e., simultaneous interactions between more than two nodes, are wide-spread in social and biological systems, and simplicial complexes, used in TDA, can capture important structural and topological properties of networks by modelling such higher-order interactions. In this position paper, we advocate for methods from TDA to be used to estimate fractal dimensions of complex networks, we discuss the possible advantages of such an approach and outline some of the challenges to be addressed.