Robustness of interdependent networks with different link patterns against cascading failures

Taking into account the load, the load redistribution, and the node capacity, we study the robustness of two interdependent networks A and B against cascading failures, where each node in network A depends on one node in network B, and vice versa. We adopt three kinds of link patterns between two interdependent networks, i.e., the assortative link (AL), the disassortative link (DL), the random link (RL), where the RA refers to connect randomly two nodes in networks A and B, the AL refers to that high-degree (low-degree) nodes in A network link high-degree (low-degree) nodes in B network, while the DL refers to the fact that high-degree nodes in A network link low-degree nodes in B network. We investigate the robustness of the interdependent networks constructed by two artificial networks and the power grid, taking into account two stages of the cascading propagation. We numerically find that both the different link patterns and the parameters in the cascading model have important effects on dramatically improving the robustness of the interdependent networks against cascading failures. In addition, we obtain the better link pattern and the matching network structure to effectively avoid the cascading propagation.