Abstract This paper extends the definition of Small-worldness to weighted complex networks and uses it to assess the robustness of Cyber-physical Critical Infrastructure Systems (CPCIS) and consequently to identify system critical components. System uncertain parameters – electric power system loading and communication network latency, are first incorporated in the model, and small-world property indices – Characteristic Path Length, Clustering Coefficient, and small-worldness are assessed in their dynamic (time-varying) forms to represent real-time uncertain criticalities, evaluated using probability distribution functions. The most critical physical and cyber system components are then identified, and their dependencies on physical and/or cyber system are identified. It was clearly demonstrated that the CPCIS components are mutually dependent on each other and that this dependency (represented by the drop of dynamic small-worldness in one system if a failure occurs in the other system) might vary from bus to bus. The proposed methodology is illustrated on a realistic interconnected 1326-bus transmission network and 88 bus star-connected ICT network, divided into 6 control zones.

中文翻译：

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使用加权复杂网络的小世界性评估网络物理系统的稳健性

摘要 本文将小世界性的定义扩展到加权复杂网络，并用它来评估信息物理关键基础设施系统（CPCIS）的鲁棒性，从而识别系统关键组件。系统不确定参数——电力系统负载和通信网络延迟，首先被纳入模型，小世界属性指数——特征路径长度、聚类系数和小世界性以其动态（时变）形式评估以表示实时的不确定临界性，使用概率分布函数进行评估。然后确定最关键的物理和网络系统组件，并确定它们对物理和/或网络系统的依赖性。已经清楚地证明了 CPCIS 组件相互依赖，并且这种依赖关系（由一个系统中的动态小世界性下降表示，如果另一个系统发生故障）可能因总线而异。所提出的方法在一个现实的互连 1326 总线传输网络和 88 总线星形连接的 ICT 网络上说明，分为 6 个控制区。