Tensor join of hypergraphs and its spectra

TL;DR

This paper introduces a tensor-based operation called tensor join for hypergraphs, demonstrating its equivalence across formulations, and explores its spectral properties and applications in constructing cospectral hypergraph pairs.

Contribution

It defines the tensor join operation on hypergraphs, proves its equivalence across three formulations, and analyzes the spectral properties and applications of hypergraphs constructed via this operation.

Findings

Tensor join unifies existing hypergraph operations.

Spectral properties of hypergraphs via tensor join are characterized.

Constructs cospectral hypergraph pairs using tensor join.

Abstract

In this paper, we introduce three operations on hypergraphs by using tensors. We show that these three formulations are equivalent and we commonly call them as the tensor join. We show that any hypergraph can be viewed as a tensor join of hypergraphs. Tensor join enable us to obtain several existing and new classes of operations on hypergraphs. We compute the adjacency, the Laplacian, the normalized Laplacian spectrum of weighted hypergraphs constructed by this tensor join. Also we deduce some results on the spectra of hypergraphs in the literature. As an application, we construct several pairs of the adjacency, the Laplacian, the normalized Laplacian cospectral hypergraphs by using the tensor join.