Percolation on interdependent networks with different group size distributions under targeted attack

Traditional research studies on interdependent networks with groups ignore the relationship between nodes in dependency groups. In real-world networks, nodes in the same group may support each other through cooperation and tend to fail or survive together. In this paper, based on the framework of group percolation, a cascading failure model on interdependent networks with cooperative dependency groups under targeted attacks is proposed, and the effect of group size distributions on the robustness of interdependent networks is investigated. The mutually giant component and phase transition point of networks with different group size distributions are analyzed. The effectiveness of the theory is verified through simulations. Results show that the robustness of interdependent networks with cooperative dependency groups can be enhanced by increasing the heterogeneity between groups under targeted attacks. The theory can well predict the numerical simulation results. This model provides some theoretical guidance for designing robust interdependent systems in real world.