Spectral properties of general hypergraphs

TL;DR

This paper explores the spectral characteristics of various tensors associated with general hypergraphs, providing bounds and characterizations that enhance understanding of their structural properties.

Contribution

It introduces new bounds for the spectral radius and characterizes odd-bipartite hypergraphs using spectral methods, extending spectral graph theory to hypergraphs.

Findings

Bounds for spectral radius based on vertex degrees

Spectral characterization of odd-bipartite hypergraphs

Analysis applicable to both uniform and non-uniform hypergraphs

Abstract

In this paper, we investigate spectral properties of the adjacency tensor, Laplacian tensor and signless Laplacian tensor of general hypergraphs (including uniform and non-uniform hypergraphs). We obtain some bounds for the spectral radius of general hypergraphs in terms of vertex degrees, and give spectral characterizations of odd-bipartite hypergraphs.