Assessment of the robustness of cyber-physical systems using small-worldness of weighted complex networks

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.