Cascading failures on interdependent hypergraph

Abstract

Scientists are aware of the importance of studying interdependent networks, as they represent real-world scenarios better than isolated networks, such as the interdependent communication and power networks. However, in real scenarios, higher-order interactions exist in these networks. Recent research has shown that higher-order interactions that cannot be reflected in simple networks (i.e., a network only has pairwise interaction) can be reflected through hypergraph. This paper proposes an interdependent hypergraph model that considers the dependencies of interlayer nodes. We studied the cascading failures in the hypergraph with different interlayer dependencies. Through theoretical analysis, we have determined the maximum attack intensity the network can withstand and how its robustness changes under different attack intensities. In completely interdependent hypergraph, the network becomes increasingly fragile as the attack intensity increases, and the final network size suddenly jumps to zero, indicating a first-order phase transition in the network. We conducted experiments on multiple artificially synthesized hypergraph. The experimental results indicate that our analytical solution is consistent with the simulated solution. These findings will help us better understand the impact of different topologies on network robustness in interdependent hypergraph, enabling us to take more effective measures to address potential network failures and attacks.