Spectra of general hypergraphs

TL;DR

This paper introduces a tensor-based method to reconstruct connectivity hypermatrices of general hypergraphs and explores their spectral properties, revealing similarities with graphs and uniform hypergraphs, thus advancing spectral hypergraph theory.

Contribution

It presents a novel tensor-based reconstruction method for hypergraph connectivity hypermatrices and analyzes their spectral properties, bridging gaps in hypergraph spectral theory.

Findings

Connectivity hypermatrices can be reconstructed using tensor methods.

Spectral properties of hypermatrices are similar across graphs and uniform hypergraphs.

The proposed representation aids future spectral hypergraph research.

Abstract

Here, we show a method to reconstruct connectivity hypermatrices of a general hypergraph (without any self loop or multiple edge) using tensor. We also study the different spectral properties of these hypermatrices and find that these properties are similar for graphs and uniform hypergraphs. The representation of a connectivity hypermatrix that is proposed here can be very useful for the further development in spectral hypergraph theory.