Cascading failures in interdependent modular networks with partial random coupling preference

Cascading failures have been widely analyzed in interdependent networks with different coupling preferences from microscopic and macroscopic perspectives in recent years. Plenty of real-world interdependent infrastructures, representing as interdependent networks, exhibit community structure, one of the most important mesoscopic structures, and partial coupling preferences, which can affect cascading failures in interdependent networks. In this paper, we propose the partial random coupling in communities, investigating cascading failures in interdependent modular scale-free networks under inner attacks and hub attacks. We mainly analyze the effects of the discoupling probability and the intermodular connection probability on cascading failures in interdependent networks. We find that increasing either the dicoupling probability or the intermodular connection probability can enhance the network robustness under both hub attacks and inner attacks. We also note that the community structure can prevent cascading failures spreading globally in entire interdependent networks. Finally, we obtain the result that if we want to efficiently improve the robustness of interdependent networks and reduce the protection cost, the intermodular connection probability should be protected preferentially, implying that improving the robustness of a single network is the fundamental method to enhance the robustness of the entire interdependent networks.