Rich-club is commonly used to describe the connectivity of a small portion of network nodes with high degrees. It is of practical importance to evaluate the impact of local rich-node connections on cascading failures of real-life interdependent networks. In this study, we present a fresh framework enabling systematic study of cascading failures in an interdependent network composed of power and communication layers with a variety of rich-clubs. The rich-clubs are classified into intra- and inter-layer ones, in which we develop a metric to quantify inter-layer rich-club connectivity. In particular, according to corresponding metrics, multiple null models are introduced using both model and real-life networks, which transform each original network into its alternative ones of varying intra- or/and inter-layer rich-clubs while preserving node degree distribution. Using a realistic cascading model with heterogeneous flow characteristics, the results show that an interdependent network with a weaker rich-club within its communication layer or a stronger inter-layer rich-club has better robustness, and simultaneously considering these two factors can make the network perform best. Our findings suggest the significant role of rich-club connectivity for designing optimization schemes against cascading failures.

中文翻译：

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Rich-Club 对相互依赖的电力和通信网络中级联故障的影响

Rich-club 常用来描述一小部分网络节点的高度连通性。评估本地富节点连接对现实生活中相互依赖的网络级联故障的影响具有实际意义。在这项研究中，我们提出了一个新的框架，可以系统地研究由电源和通信层与各种富俱乐部组成的相互依赖的网络中的级联故障。富俱乐部分为层内和层间，我们在其中开发了一个度量来量化层间富俱乐部的连通性。特别是，根据相应的指标，使用模型和现实生活网络引入多个空模型，它将每个原始网络转换为不同的层内或/和层间富俱乐部的替代网络，同时保留节点度分布。使用具有异构流特征的现实级联模型，结果表明，在其通信层内具有较弱rich-club或层间rich-club较强的相互依赖网络具有更好的鲁棒性，同时考虑这两个因素可以使网络表现最好。我们的研究结果表明，富俱乐部连接性对于设计针对级联故障的优化方案具有重要作用。同时考虑这两个因素可以使网络表现最好。我们的研究结果表明，富俱乐部连接性对于设计针对级联故障的优化方案具有重要作用。同时考虑这两个因素可以使网络表现最好。我们的研究结果表明，富俱乐部连接性对于设计针对级联故障的优化方案具有重要作用。