Fractal dimensions of complex networks: advocating for a topological approach

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Bibliographic Details
Main Authors:	Andreeva, Rayna, Contreras-Peruyero, Haydeé, Krishnagopal, Sanjukta, Otter, Nina, Pascali, Maria Antonietta, Thompson, Elizabeth
Format:	Preprint
Published:	2025
Subjects:	Algebraic Topology Discrete Mathematics
Online Access:	Acceder al recurso
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author	Andreeva, Rayna Contreras-Peruyero, Haydeé Krishnagopal, Sanjukta Otter, Nina Pascali, Maria Antonietta Thompson, Elizabeth
author_facet	Andreeva, Rayna Contreras-Peruyero, Haydeé Krishnagopal, Sanjukta Otter, Nina Pascali, Maria Antonietta Thompson, Elizabeth
contents	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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2506_15236
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Fractal dimensions of complex networks: advocating for a topological approach Andreeva, Rayna Contreras-Peruyero, Haydeé Krishnagopal, Sanjukta Otter, Nina Pascali, Maria Antonietta Thompson, Elizabeth Algebraic Topology Discrete Mathematics 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.
title	Fractal dimensions of complex networks: advocating for a topological approach
topic	Algebraic Topology Discrete Mathematics
url	https://arxiv.org/abs/2506.15236

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