College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China.
School of Public Health, Chongqing Medical University, Chongqing 400016, China.
Chaos. 2022 Jul;32(7):073121. doi: 10.1063/5.0090626.
In modern systems, from brain neural networks to social group networks, pairwise interactions are not sufficient to express higher-order relationships. The smallest unit of their internal function is not composed of a single functional node but results from multiple functional nodes acting together. Therefore, researchers adopt the hypergraph to describe complex systems. The targeted attack on random hypergraph networks is still a problem worthy of study. This work puts forward a theoretical framework to analyze the robustness of random hypergraph networks under the background of a targeted attack on nodes with high or low hyperdegrees. We discovered the process of cascading failures and the giant connected cluster (GCC) of the hypergraph network under targeted attack by associating the simple mapping of the factor graph with the hypergraph and using percolation theory and generating function. On random hypergraph networks, we do Monte-Carlo simulations and find that the theoretical findings match the simulation results. Similarly, targeted attacks are more effective than random failures in disintegrating random hypergraph networks. The threshold of the hypergraph network grows as the probability of high hyperdegree nodes being deleted increases, indicating that the network's resilience becomes more fragile. When considering real-world scenarios, our conclusions are validated by real-world hypergraph networks. These findings will help us understand the impact of the hypergraph's underlying structure on network resilience.
在现代系统中，从脑神经网络到社会群体网络，成对的相互作用不足以表达高阶关系。其内部功能的最小单元不是由单个功能节点组成，而是由多个功能节点共同作用产生的。因此，研究人员采用超图来描述复杂系统。针对随机超图网络的有目标攻击仍然是一个值得研究的问题。这项工作提出了一个理论框架，在节点的高或低超度数的有目标攻击的背景下，分析随机超图网络的鲁棒性。我们通过将因子图的简单映射与超图联系起来，并利用渗流理论和生成函数，发现了超图网络在有目标攻击下的级联故障和巨大连通簇（GCC）的过程。在随机超图网络上，我们进行了蒙特卡罗模拟，并发现理论发现与模拟结果相符。同样，在破坏随机超图网络方面，有目标攻击比随机故障更为有效。随着删除高超度数节点的概率增加，超图网络的阈值增加，表明网络的弹性变得更加脆弱。在考虑真实场景时，我们通过真实的超图网络验证了我们的结论。这些发现将有助于我们理解超图的底层结构对网络弹性的影响。
