Evolving Networks with Enhanced Stability Properties

We use a search algorithm to identify networks with enhanced linear stability properties in this account. We then analyze these networks for topological regularities that explain the source of their stability/instability. Analysis of the structure of networks with enhanced stability properties reveals that these networks are characterized by a highly skewed degree distribution, very short path-length between nodes, little or no clustering, and dissasortativity. By contrast, networks with enhanced instability properties have a peaked degree distribution with a small variance, long path-lengths between nodes, a high degree of clustering, and high assortativity. 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, while networks with enhanced instability properties are robust to targeted attacks. These network features have implications for the physical and biological networks that surround us.