Cavity analysis on the robustness of random networks against targeted attacks: Influences of degree-degree correlations

We developed a scheme for evaluating the size of the largest connected subnetwork (giant component) in random networks and the percolation threshold when sites (nodes) and/or bonds (edges) are removed from the networks based on the cavity method of statistical mechanics of disordered systems. We apply our scheme particularly to random networks of bimodal degree distribution (two-peak networks), which have been proposed in earlier studies as robust networks against random failures of site and/or targeted (random degree-dependent) attacks on sites. Our analysis indicates that the correlations among degrees affect a network's robustness against targeted attacks on sites or bonds nontrivially depending on details of network configurations.