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.

中文翻译：

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相互依赖的超图上的级联故障


科学家们意识到研究相互依赖的网络的重要性，因为它们比孤立的网络（例如相互依赖的通信和电力网络）更好地代表了现实世界的场景。然而，在实际场景中，这些网络中存在高阶交互。最近的研究表明，简单网络中无法反映的高阶交互（即网络仅具有成对交互）可以通过超图来反映。本文提出了一种考虑层间节点依赖关系的相互依赖超图模型。我们研究了具有不同层间依赖关系的超图中的级联故障。通过理论分析，我们确定了网络能够承受的最大攻击强度以及在不同攻击强度下其鲁棒性如何变化。在完全相互依赖的超图中，随着攻击强度的增加，网络变得越来越脆弱，最终的网络大小突然跳至零，表明网络中存在一阶相变。我们对多个人工合成的超图进行了实验。实验结果表明我们的解析解与模拟解是一致的。这些发现将帮助我们更好地理解不同拓扑对相互依赖的超图中网络鲁棒性的影响，使我们能够采取更有效的措施来解决潜在的网络故障和攻击。