The magnitude homology of a hypergraph
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929642819026944 |
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| author | Bi, Wanying Li, Jingyan Wu, Jie |
| author_facet | Bi, Wanying Li, Jingyan Wu, Jie |
| contents | The magnitude homology, introduced by R. Hepworth and S. Willerton, offers a topological invariant that enables the study of graph properties. Hypergraphs, being a generalization of graphs, serve as popular mathematical models for data with higher-order structures. In this paper, we focus on describing the topological characteristics of hypergraphs by considering their magnitude homology. We begin by examining the distances between hyperedges in a hypergraph and establish the magnitude homology of hypergraphs. Additionally, we explore the relationship between the magnitude and the magnitude homology of hypergraphs. Furthermore, we derive several functorial properties of the magnitude homology for hypergraphs. Lastly, we present the Künneth theorem for the simple magnitude homology of hypergraphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_01534 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The magnitude homology of a hypergraph Bi, Wanying Li, Jingyan Wu, Jie Algebraic Topology The magnitude homology, introduced by R. Hepworth and S. Willerton, offers a topological invariant that enables the study of graph properties. Hypergraphs, being a generalization of graphs, serve as popular mathematical models for data with higher-order structures. In this paper, we focus on describing the topological characteristics of hypergraphs by considering their magnitude homology. We begin by examining the distances between hyperedges in a hypergraph and establish the magnitude homology of hypergraphs. Additionally, we explore the relationship between the magnitude and the magnitude homology of hypergraphs. Furthermore, we derive several functorial properties of the magnitude homology for hypergraphs. Lastly, we present the Künneth theorem for the simple magnitude homology of hypergraphs. |
| title | The magnitude homology of a hypergraph |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2306.01534 |