Evolving Networks with Enhanced Linear Stability Properties

Abstract

Networks are so much a part of our modern society that when they fail the effects can be significant. In many cases, global network failures can be triggered by seemingly minor local events. Increased understanding of why this occurs and, importantly, the properties of the network that allow it to occur, is thus desirable. In this account we use an evolutionary algorithm to evolve complex networks that have enhanced linear stability properties. We then analyze these networks for topological regularities that explain the source their stability/instability. Analysis of the structure of networks with enhanced stability properties reveals that these networks have a highly skewed degree distribution, very short path-length between nodes, have little or no clustering and are dissasortative. By contrast, networks with enhanced instability properties have a peaked degree distribution with a small variance, have long path-lengths between nodes, contain a high degree of clustering and are highly assortative. We then test the topological stability of these networks and discover that networks with enhanced stability properties are highly robust to the random removal of nodes, but highly fragile to targeted attacks. Networks with enhanced instability properties are robust to targeted attacks. These network features have implications for the physical and biological networks that surround us.