Geodesic
The magnitude homology of a hypergraph
Homology, homotopy, and applications, Tome 26 (2024) no. 2, pp. 325-348.

Voir la notice de l'article provenant de la source International Press of Boston

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.
DOI : 10.4310/HHA.2024.v26.n2.a16
Classification : 05C65, 55N35, 55U25
Keywords: hypergraph, magnitude, magnitude homology, Künneth theorem 
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Wanying Bi; Jingyan Li; Jie Wu. The magnitude homology of a hypergraph. Homology, homotopy, and applications, Tome 26 (2024) no. 2, pp. 325-348. doi : 10.4310/HHA.2024.v26.n2.a16. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2024.v26.n2.a16/

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