Robustness envelopes of networks

We study the robustness of networks under node removal, considering random node failure, as well as targeted node attacks based on network centrality measures. Whilst both of these have been studied in the literature, existing approaches tend to study random failure in terms of average-case behavior, giving no idea of how badly network performance can degrade purely by chance. Instead of considering average network performance under random failure, we compute approximate network performance probability density functions as functions of the fraction of nodes removed. We find that targeted attacks based on centrality measures give a good indication of the worst-case behavior of a network. We show that many centrality measures produce similar targeted attacks and that a combination of degree centrality and eigenvector centrality may be enough to evaluate worst-case behavior of networks. Finally, we study the robustness envelope and targeted attack responses of networks that are rewired to have high-and lowdegree assortativities, discovering that moderate assortativity increases confer more robustness against targeted attacks whilst moderate decreases confer more robustness against random uniform attacks.