Robustness of hybrid interdependent higher-order networks

In recent decades, researchers have used interdependent networks and interdependent higher-order networks to model real-world interdependent systems that exhibit only low-order (pairwise interactions) or higher-order relationships. However, in real life, both higher-order and low-order relationships often coexist. For example, in a Cyber-Physical System (CPS), the communication relationships between nodes in the network layer represent low-order relations, whereas the collection of devices located within the same physical area in the physical layer constitutes higher-order relations. Therefore, this paper investigates a hybrid interdependent higher-order network model that incorporates both low-order and higher-order relationships, with the latter represented by a hypergraph. By randomly removing nodes from the network, we systematically analyze the robustness of this model. A unified theoretical framework is proposed, and experiments are conducted on artificial and real-world networks with different topological structures. The experimental results show that the theoretical predictions are highly consistent with the simulation results. These findings not only deepen our understanding of the robustness of hybrid interdependent higher-order networks but also provide new theoretical insights for preventing failures in such networks.