Robustness Sensitivities in Large Networks

Abstract

This article focuses on developing a framework to assess robustness in large interconnected networks that arise frequently in many socioeconomic networks such as transportation, economics, and opinion dynamics. We first introduce the idea of “asymptotic” resilience, i.e., a measure of robustness to disturbances, as the network size increases, keeping the underlying structure invariant. We argue that such a notion of robustness is different from existing ideas in robust control theory that do not account for network topology and dimension. Under this new framework, we formulate a hierarchy of resilience for different network topologies. We present examples of commonly encountered network topologies and comment on their resilience. We then provide a formal characterization of how edge link perturbation affects resilience in large networks. Further, we show how each node of the network contributes to its resilience and identify critical nodes that become “fragile” as the network dimension grows. A major contribution of our work is that the analysis is no longer limited to undirected networks, as in previous literature.