Recent work on the cascading failure of networks with dependence groups assumes that the number of nodes in each dependence group is equal. In this paper, we construct a model on interdependent networks with dependence groups against cascading failure. The size of dependence group is supposed to obey the Poisson Distribution and the Truncated Normal Distribution, respectively. By applying the tools of mean-field approximation and the generating function techniques, the cascading model is theoretically analyzed and the theoretical solutions are nearly consistent with the simulation values. Besides, we define three kinds of coupling preferences based on node degree, i.e. assortative coupling, disassortative coupling and random coupling. The connection between layers is no longer one-to-one correspondence of nodes, but fully connection of some groups. In addition, some factors affecting the network robustness are discussed and extensive simulations are realized on two-layer BA networks. The simulation results show that the coupling preference has influence on the network robustness and the network with dependence groups obeying the Truncated Normal Distribution performs better than the Poisson Distribution.

中文翻译：

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依赖组服从不同分布的相互依赖网络的级联故障

最近关于具有依赖组的网络的级联故障的工作假设每个依赖组中的节点数量是相等的。在本文中，我们构建了一个具有依赖组以防止级联故障的相互依赖网络模型。依赖组的大小应该分别服从泊松分布和截断正态分布。应用平均场逼近工具和生成函数技术，对级联模型进行了理论分析，理论解与仿真值基本一致。此外，我们根据节点度定义了三种耦合偏好，即分类耦合、不分类耦合和随机耦合。层与层之间的连接不再是节点的一一对应，而是部分组的全连接。此外，讨论了影响网络鲁棒性的一些因素，并在两层BA网络上实现了广泛的模拟。仿真结果表明，耦合偏好对网络鲁棒性有影响，依赖组服从截断正态分布的网络性能优于泊松分布。