Spontaneous recovery in random hypergraphs.

In many real-world phenomena, such as the reconstruction of disaster areas after an earthquake or the stock market's recovery after an economic crisis, damaged networks are spontaneously active after receiving assistance. To reveal how the recovery process, the research of dynamic network recovery has become a hot topic in the field of network science. Previous studies on network recovery have been limited to simple networks with pairwise interactions. However, real-world systems are usually networks with higher-order interactions that are composed of multiple units. To better understand the recovery phenomenon on complex networks in the real world, we propose a novel spontaneous recovery model applied to hypergraphs. The model considers two types of recovery, internal recovery and fast recovery, where inactive nodes in the network can either recover internally with independent probabilities or receive sufficient resources from the hyperedge for fast recovery. We find that the number of active nodes in the system shows a phase change from continuous to discontinuous as the fast recovery condition is relaxed. Moreover, under the influence of higher-order interactions, increasing both average hyperedge cardinality and network heterogeneity contribute to increasing the network resilience. These findings help us understand the recovery mechanisms of complex networks and provide essential insights into designing highly resilient systems.