Breakdown in interdependent directed networks under targeted attacks

Cascading failures take place between networks after initial failures occur in interdependent networks. Most previous studies are limited to undirected networks, while many real-world networks are directed. For interdependent directed networks, earlier studies focused on random initial failures. How the interdependent directed networks respond to targeted attacks has not been addressed. In this work, we develop a general theoretical framework for analyzing the robustness in interdependent directed networks under targeted attack on nodes with high or low degrees (in-degrees or out-degrees). We find that for degree heterogeneous networks, targeted attacks perform more efficiently in breaking down the system than random failures, with the degree-based attacks being the most efficient way. Interestingly, we find that system robustness first increases then decreases as the degree heterogeneity increases, showing a peak, which helps understand system robustness and enables the better design of robust infrastructure systems