Structural Robustness and Vulnerability of Networks

TL;DR

This paper reviews various notions of network robustness across disciplines, categorizing them within a framework to clarify apparent contradictions and guide future research in designing robustness experiments.

Contribution

It provides a comprehensive survey of network robustness measures, clarifies their applicability, and offers practical guidance for experimental design in this field.

Findings

Different robustness notions can yield similar results under certain conditions.

The survey clarifies when specific robustness measures are appropriate.

Practical guidelines for designing robustness experiments are proposed.

Abstract

Networks are useful descriptions of the structure of many complex systems. Unsurprisingly, it is thus important to analyze the robustness of networks in many scientific disciplines. In applications in communication, logistics, finance, ecology, biomedicine, and many other fields, researchers have studied the robustness of networks to the removal of nodes, edges, or other subnetworks to identify and characterize robust network structures. A major challenge in the study of network robustness is that researchers have reported that different and seemingly contradictory network properties are correlated with a network's robustness. Using a framework by Alderson and Doyle~\cite{Alderson2010}, we categorize several notions of network robustness and we examine these ostensible contradictions. We survey studies of network robustness with a focus on (1)~identifying robustness specifications in common use, (2)~understanding when these specifications are appropriate, and (3)~understanding the conditions under which one can expect different notions of robustness to yield similar results. With this review, we aim to give researchers an overview of the large, interdisciplinary body of work on network robustness and develop practical guidance for the design of computational experiments to study a network's robustness.