Fractal dimensions of complex networks: advocating for a topological approach
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.
Keywords
Cite
@article{arxiv.2506.15236,
title = {Fractal dimensions of complex networks: advocating for a topological approach},
author = {Rayna Andreeva and Haydeé Contreras-Peruyero and Sanjukta Krishnagopal and Nina Otter and Maria Antonietta Pascali and Elizabeth Thompson},
journal= {arXiv preprint arXiv:2506.15236},
year = {2025}
}
Comments
to appear in 3rd WinCompTop proceedings (AWM-IMA Springer volume "Research in Computational Topology")