The embedded homology of hypergraphs and applications
By S. Bressan, Jingyan Li, S. Ren, Jie Wu. Asian Journal of Mathematics, 2016
61 citations recorded by the source corpus.
Hypergraphs are mathematical models for many problems in data sciences. In recent decades, the topological properties of hypergraphs have been studied and various kinds of (co)homologies have been constructed (cf. [3, 4, 12]). In this paper, generalising the usual homology of simplicial complexes, we define the embedded homology of hypergraphs as well as the persistent embedded homology of sequences of hypergraphs. As a generalisation of the Mayer-Vietoris sequence for the homology of simplicial complexes, we give a Mayer-Vietoris sequence for the embedded homology of hypergraphs. Moreover, as applications of the embedded homology, we study acyclic hypergraphs and construct some indices for the data analysis of hyper-networks.
Subfields: Biological Psychiatry, Computational Theory and Mathematics, Physiology
View Paper: https://www.semanticscholar.org/paper/501e10752f6a4f0d5efcd56d63811fad4dc8ad05
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In Computational Theory and Mathematics
Citations in the corpus
- What are higher-order networks? (2021, background): “Hypergraph data can be analyzed with homology [43] or persistent homology [225]; however, the applications discussed in this section focus on simplicial complexes or”