A comparative study on the variants of R metric for network robustness

Robust network infrastructures are essential for the delivery of vital services for our daily lives. With the widespread cyber-attacks on them, measuring the robustness of these networks has become an important issue. In recent years, many robustness metrics have been proposed for this purpose. Among them, a metric called 'R' has received wide attention, and several variants have been proposed. These variants include a metric called Communication Robustness (CR) and the betweenness and closeness variants to both R and CR. However, no evaluations about the correlations among these variants have been made to shed light on their necessity and effectiveness. Addressing this research gap, this paper makes the following contributions. First, we measure the correlations between R and CR to verify that CR is valid to exist due to its unique perspective although it correlates closely with R. Second, we measure the correlations between R and its betweenness/closeness variants to show that they are quite different, and the same is observed for CR and its betweenness/closeness variants. Finally, we propose a new robustness metric called Simplified Communication Robustness (SCR), which simplifies the calculation of CR while working almost the same as CR.