On The Discrete Morse Functions for Hypergraphs

TL;DR

This paper extends discrete Morse theory to hypergraphs by analyzing their embedded homology and associated simplicial complexes, providing new tools for topological analysis of hypergraph structures.

Contribution

It generalizes discrete Morse functions from simplicial complexes to hypergraphs and their associated complexes, enhancing topological methods for hypergraph analysis.

Findings

Generalized discrete Morse functions to hypergraphs

Analyzed embedded homology of hypergraphs

Connected hypergraph homology with associated simplicial complexes

Abstract

A hypergraph can be obtained from a simplicial complex by deleting some non-maximal simplices. In this paper, we study the embedded homology as well as the homology of the (lower-)associated simplicial complexes for hypergraphs. We generalize the discrete Morse functions on simplicial complexes. We study the discrete Morse functions on hypergraphs as well as the discrete Morse functions on the (lower-)associated simplicial complexes of the hypergraphs.