Comparing the reliability of networks by spectral analysis

TL;DR

This paper introduces a spectral analysis method based on the Cheeger constant to rank network reliability, validated across various network types including real-world and synthetic models.

Contribution

It presents a novel spectral ranking approach for network reliability that leverages the Cheeger constant and eigenvalue gaps, applicable to diverse network structures.

Findings

Eigenvalue gaps effectively rank network reliability.

Method successfully applied to IEEE57, Erdős-Rényi, and Small-World networks.

Spectral analysis provides a reliable measure of network robustness.

Abstract

We provide a method for the ranking of the reliability of two networks with the same connectance. Our method is based on the Cheeger constant linking the topological property of a network with its spectrum. We first analyze a set of twisted rings with the same connectance and degree distribution, and obtain the ranking of their reliability using their eigenvalue gaps. The results are generalized to general networks using the method of rewiring. The success of our ranking method is verified numerically for the IEEE57, the Erd\H{o}s-R\'enyi, and the Small-World networks.