Finding the Cores of Higher Graphs Using Geometric and Topological Means: A Survey
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918073258213376 |
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| author | García-Redondo, Inés Landi, Claudia Percival, Sarah Skeja, Anda Wang, Bei Zhou, Ling |
| author_facet | García-Redondo, Inés Landi, Claudia Percival, Sarah Skeja, Anda Wang, Bei Zhou, Ling |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19857 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finding the Cores of Higher Graphs Using Geometric and Topological Means: A Survey García-Redondo, Inés Landi, Claudia Percival, Sarah Skeja, Anda Wang, Bei Zhou, Ling History and Overview Computational Geometry Discrete Mathematics Combinatorics 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. |
| title | Finding the Cores of Higher Graphs Using Geometric and Topological Means: A Survey |
| topic | History and Overview Computational Geometry Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2506.19857 |