All eigenvalues of the power hypergraph and signed subgraphs of a graph

TL;DR

This paper demonstrates how to derive all eigenvalues of a power hypergraph from the eigenvalues of signed subgraphs of the original graph, correcting a previous error in the literature.

Contribution

It provides a new method to compute hypergraph eigenvalues from graph eigenvalues, fixing an earlier incorrect statement.

Findings

All eigenvalues of power hypergraphs can be generated from signed subgraphs.

Corrects a previous incorrect claim about eigenvalues of power hypergraphs.

Provides a theoretical framework linking graph and hypergraph spectra.

Abstract

We show how all eigenvalues of a power hypergraph $G^{(k)}$ can be generated from the eigenvalues of signed subgraphs of the underlying graph $G$. This fixes an incorrect statement in the case of power hypergraphs from [Linear Algebra and its Applications, 590:243-257, 2020].