Spectral theory of weighted hypergraphs via tensors

TL;DR

This paper explores how the spectral properties of tensors associated with weighted hypergraphs reveal structural information, and introduces efficient methods for computing eigenvalues using numerical algebraic geometry.

Contribution

It provides a novel analysis linking hypergraph properties to tensor eigenvalues and presents efficient computational techniques for eigenvalue calculation.

Findings

Eigenvalues reflect hypergraph structure

Efficient eigenvalue computation methods introduced

Spectral properties encode hypergraph information

Abstract

One way to study an hypergraph is to attach to it a tensor. Tensors are a generalization of matrices, and they are an efficient way to encode information in a compact form. In this paper we study how properties of weighted hypergraphs are reflected on eigenvalues and eigenvectors of their associated tensors. We also show how to efficiently compute eingenvalues with some techniques from numerical algebraic geometry.