Finding the Cores of Higher Graphs Using Geometric and Topological Means: A Survey
History and Overview
2025-06-30 v1 Computational Geometry
Discrete Mathematics
Combinatorics
Abstract
In this survey, we explore recent literature on finding the cores of higher graphs using geometric and topological means. We study graphs, hypergraphs, and simplicial complexes, all of which are models of higher graphs. We study the notion of a core, which is a minimalist representation of a higher graph that retains its geometric or topological information. We focus on geometric and topological methods based on discrete curvatures, effective resistance, and persistent homology. We aim to connect tools from graph theory, discrete geometry, and computational topology to inspire new research on the simplification of higher graphs.
Cite
@article{arxiv.2506.19857,
title = {Finding the Cores of Higher Graphs Using Geometric and Topological Means: A Survey},
author = {Inés García-Redondo and Claudia Landi and Sarah Percival and Anda Skeja and Bei Wang and Ling Zhou},
journal= {arXiv preprint arXiv:2506.19857},
year = {2025}
}
Comments
54 pages