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.

在相互依赖的网络中发生初始故障之后，网络之间会发生级联故障。大多数以前的研究仅限于无向网络，而许多现实世界的网络是有向的。对于相互依赖的有向网络，早期的研究集中在随机初始故障上。相互依赖的定向网络如何响应目标攻击尚未得到解决。在这项工作中，我们开发了一个通用的理论框架，用于分析在对高或低度（入度或出度）节点进行针对性攻击的情况下相互依赖的有向网络的鲁棒性。我们发现，对于程度异构网络，有针对性的攻击比随机故障更有效地破坏系统，基于程度的攻击是最有效的方式。有趣的是，