The Embedded Homology of Hypergraphs and Applications
Algebraic Topology
2018-03-15 v5
Abstract
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.
Keywords
Cite
@article{arxiv.1610.00890,
title = {The Embedded Homology of Hypergraphs and Applications},
author = {Stephane Bressan and Jingyan Li and Shiquan Ren and Jie Wu},
journal= {arXiv preprint arXiv:1610.00890},
year = {2018}
}
Comments
20 pages