2020/02/06 by Shiquan Ren, Jie Wu, Ren, Shiquan +1
Computer Science · Mathematics · Medicine · #Algebraic Topology (math.AT) #Alzheimer's disease research and treatments #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2002.02237
openalex publication_date 2020/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Hypergraph is the most general model for complex networks involving group interactions. Taking the ideas of path homology from Alexander Grigor'yan, Yong Lin, Yuri Muranov and Shing-Tung Yau [18-22], Stephane Bressan, Jingyan Li and the authors of this article introduced embedded homology of hypergraphs [6] in 2019, which has leaded to successful applications in protein-ligand binding network [24, 25] in 2021. A fundamental question arising from practical applications is about the stability of the persistent embedded homology of hypergraphs. In this paper, we prove the stability of the persistent embedded homology as well as the persistent homology of the associated simplicial complex with respect to perturbations of the filtration on a hypergraph. We apply the persistent homology methods to morphisms of hypergraphs and prove the stability with respect to perturbations of the filtrations. We prove the constancy of the persistent Betti numbers under some conditions on the simple-homotopy types of hypergraphs.