Laplacians on quantum hypergraphs

TL;DR

This paper introduces quantum hypergraphs, extending the concept of quantum graphs, and discusses the challenges in defining a Laplacian operator on hypergraphs.

Contribution

It proposes the framework of quantum hypergraphs and highlights the key issues in formulating a Laplacian on these structures.

Findings

Identification of problems in defining Laplacians on hypergraphs

Extension of quantum graph theory to hypergraphs

Foundation for future research on quantum hypergraph operators

Abstract

We introduce quantum hypergraphs, in analogy with the theory of quantum graphs developed over the last 15 years by many authors. We emphasize some problems that arise when one tries to define a Laplacian on a hypergraph.