Modeling and analysis of cascading failures in multilayer higher-order networks

With the increasing application of network science, understanding the behavior of higher-order networks has become particularly important. Especially, the study of multilayer higher-order networks is significant for revealing the interdependence and higher-order interactions in complex systems. This paper proposes a mathematical framework to explore multilayer higher-order networks composed of multiple fully interdependent hypergraphs. Each hypergraph consists of the same number of nodes, and nodes between layers are connected one-to-one. By analyzing the cascading failures of multilayer hypergraphs under different topologies, we found that although the network sizes are the same in the steady state, different topological structures (such as star-like, tree-like, and chain-like) significantly affect the time required to reach a stable state, with the star-like topology reaching stability the fastest. Furthermore, we explored the impact of network parameters on the robustness of networks. We found that in multilayer homogeneous hypergraphs, the robustness of the network becomes stronger with an increase in the average hyperdegree or average hyperedge cardinality; in multilayer heterogeneous hypergraphs, the robustness of the network becomes more fragile as the power exponent increases. Finally, experimental results indicate that with the rise in the number of network layers, the network becomes more fragile.