Graph measures and network robustness

TL;DR

This paper surveys various graph-based measures such as connectivity, distance, betweenness, clustering, and spectral properties to evaluate and compare the robustness of simple, undirected, unweighted networks, aiding network design and improvement.

Contribution

It provides a comprehensive overview of existing robustness measures and discusses their effectiveness in assessing network resilience against failures or attacks.

Findings

Spectral measures based on Laplacian eigenvalues are effective for robustness evaluation.

Connectivity and betweenness measures correlate with network resilience.

The survey offers practical tools for network administrators to enhance robustness.

Abstract

Network robustness research aims at finding a measure to quantify network robustness. Once such a measure has been established, we will be able to compare networks, to improve existing networks and to design new networks that are able to continue to perform well when it is subject to failures or attacks. In this paper we survey a large amount of robustness measures on simple, undirected and unweighted graphs, in order to offer a tool for network administrators to evaluate and improve the robustness of their network. The measures discussed in this paper are based on the concepts of connectivity (including reliability polynomials), distance, betweenness and clustering. Some other measures are notions from spectral graph theory, more precisely, they are functions of the Laplacian eigenvalues. In addition to surveying these graph measures, the paper also contains a discussion of their functionality as a measure for topological network robustness.