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The embedded homology of hypergraphs and applications
Asian Journal of Mathematics ( IF 0.6 ) Pub Date : 2019-01-01 , DOI: 10.4310/ajm.2019.v23.n3.a6
Stephane Bressan 1 , Jingyan Li 2 , Shiquan Ren 3 , Jie Wu 4
Affiliation  

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.

中文翻译:

超图与应用的嵌入同源性

超图是数据科学中许多问题的数学模型。近几十年来,人们研究了超图的拓扑性质,并构建了各种(共)同调(参见 [3, 4, 12])。在本文中,概括单纯复形的通常同源性,我们定义了超图的嵌入同源性以及超图序列的持久嵌入同源性。作为单纯复形同源性的 Mayer-Vietoris 序列的推广,我们给出了嵌入超图同源性的 Mayer-Vietoris 序列。此外,作为嵌入同源性的应用,我们研究了无环超图并构建了一些用于超网络数据分析的指标。
更新日期:2019-01-01
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