Supersymmetry on Graphs and Networks

TL;DR

This paper reveals a natural supersymmetric structure in graphs and networks, enabling the derivation of spectral properties that relate to key graph characteristics, with potential implications for physical applications.

Contribution

It introduces a supersymmetric framework for analyzing graphs and networks, providing new spectral insights not previously available.

Findings

Spectral properties of graph operators are derived using supersymmetry.

Supersymmetry offers a novel perspective on graph characteristics.

Potential applications in physical systems are suggested.

Abstract

We show that graphs, networks and other related discrete model systems carry a natural supersymmetric structure, which, apart from its conceptual importance as to possible physical applications, allows to derive a series of spectral properties for a class of graph operators which typically encode relevant graph characteristics.