Percolation of interdependent networks with degree-correlated inter-connections

In interdependent networks, failures of nodes in one constituent network lead nodes in another network to fail. This happens recursively and leads to a cascade of failures. It is known that the interdependent networks with random inter-connections have weaker robustness than the individual networks. However, if the interdependent networks have degree correlations between the networks constructing them as in the actual cases, the robustness of the interdependent networks may be changed. In this paper, we perform numerical simulations on interdependent networks and obtain the giant cluster sizes after the cascade of failures in order to evaluate the robustness. We show that when a interdependent network has a positive degree inter-correlation, it has the stronger robustness than that for the networks with no degree correlation. We show not only the numerical simulation results but theoretical ones for the robustness of the interdependent networks.