Analysis on Cascading Failures of Directed–Undirected Interdependent Networks with Different Coupling Patterns

Most existing studies model interdependent networks as simple network systems consisting of two or more undirected subnets, and the interdependent edges between the networks are undirected. However, many real-world interdependent networks are coupled by a directed subnet and an undirected subnet, such as supply chain networks coupled with cyber networks, and cyber manufacturing networks coupled with service networks. Therefore, in this work, we focus on a ubiquitous type of interdependent network—the directed–undirected interdependent network—and research the cascading failures of directed–undirected interdependent networks with different coupling patterns. Owing to the diversity of coupling patterns to realistic interdependent network systems, we introduce two types of interdependent edges (i.e., directed-to-undirected and undirected-to-directed interdependent edges). On this basis, we generated different types of directed–undirected interdependent networks with varying coupling patterns (i.e., one-to-one, one-to-many, and many-to-one) and investigated the cascading failure robustness of these types of networks. Finally, we explored the cascading robustness of directed–undirected interdependent networks under two different attack strategies (single-node attack and multi-node attack). Through extensive experiments, we have obtained some meaningful findings: (1) the cascading robustness of directed–undirected interdependent networks is positively related to the overload tolerance coefficient and load exponential coefficient; (2) high-degree nodes and high-in-degree nodes should be protected to improve the cascading robustness of directed–undirected interdependent networks; (3) the cascading robustness of one-to-many interdependent networks can be improved by adding directed-to-undirected interdependent edges; and the cascading robustness of many-to-one interdependent networks can be improved by adding undirected-to-directed interdependent edges.