Normalized Laplace Operators for Hypergraphs with Real Coefficients

TL;DR

This paper extends the theory of normalized Laplace operators to hypergraphs with real coefficients, analyzing how hypergraph symmetries influence the spectral properties of these operators.

Contribution

It introduces a generalized framework for normalized Laplace operators on hypergraphs with real coefficients and investigates the impact of hypergraph symmetries on their spectra.

Findings

Symmetries significantly affect the spectrum of the Laplacian.

Generalization to real coefficients broadens applicability.

Spectral properties linked to hypergraph structure.

Abstract

Chemical hypergraphs and their associated normalized Laplace operators are generalized and studied in the case where each vertex--hyperedge incidence has a real coefficient. We systematically study the effect of symmetries of a hypergraph on the spectrum of the Laplacian.