Asian Journal of Mathematics
Volume 23 (2019)
The embedded homology of hypergraphs and applications
Pages: 479 – 500
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. [4, 7, 19]). 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.
hypergraph, acyclic hypergraph, homology, persistent homology, Mayer–Vietoris sequence, hyper-network
2010 Mathematics Subject Classification
Primary 55U10, 55U15. Secondary 68P05, 68P15.
This work was supported by the National Research Foundation, Prime Minister’s Office, Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) programme.
Received 4 October 2016
Accepted 14 February 2018
Published 9 July 2019