Resilience of interdependent hypergraphs in failure–recovery spreading process

In many real-world networked systems, failed nodes can recover from failures after being repaired. Existing studies on failure–recovery dynamics in networks focus on single networks, while rich data have revealed that empirical complex systems exhibit higher-order dependencies among nodes such as multi-type and group interactions. In this paper, we propose a failure–recovery spreading model in interdependent hypergraphs and study the resilience of the hypergraphs. In this model, active nodes fail randomly at a certain rate and propagate the failure to their interdependent nodes through interdependent edges. A failed node recover spontaneously or be restored by participating in enough active hyperedges. By using the mean-field method, we analyze the resilience of the interdependent hypergraphs. It is found that increasing the average hyperedge cardinality can enhance the resilience of the system, and increasing network heterogeneity causes the phase transition of the system disappear. Increasing the failure rate of interdependent nodes through interdependent links reduces the resilience of the system, and a discontinuous phase transition appears. There exists a critical threshold of the fraction of active hyperedges above which the participating failed nodes will be restored, and the system enters a low-activity state. For the interdependent hypergraphs consisting of a network with homogeneous hyperedge cardinality distribution and a network with heterogeneous hyperedge cardinality distribution, due to the interlayer dependencies and difference in resilience of each layer, rich phenomena are found as the failure rates vary. These findings help us better understand the resilience of interdependent hypergraphs under failure–recovery dynamics.