Assessing the Applicability of Complex Network Theory Models and Importance Measures to Vulnerability Studies of Cyber-physical Systems

Calculating centrality measures has been used to identify Cyber-physical System critical component for some time. However, accurate identification of critical elements within the interconnected system that are vulnerable to system failures and intentional attacks requires not only a reliable model but robust index to dynamic system operating environment. These measures include 1) Node Degree, 2) Node Importance, 3) Betweenness Centrality, 4) Closeness Centrality and 5) Eigenvector Centrality. System component criticalities have been evaluated based on these measures in this paper and their performances and rankings under different network topologies and operating conditions have been compared using 1) Pearson Correlation Coefficient and 2) Spearman Correlation Coefficient. This has enabled the quantification of the optimality of using different centrality measures in different network scenarios. The results suggest that Betweenness and Degree centralities are the most suitable indices for identifying critical electrical power system bus and cyber system node individually. Moreover, the degree of correlation between directed measures has suggested also the necessity of using directional model in Cyber-physical System studies.