Resilience-based network component importance measures

Disruptive events, whether malevolent attacks, natural disasters, manmade accidents, or common failures, can have significant widespread impacts when they lead to the failure of network components and ultimately the larger network itself. An important consideration in the behavior of a network following disruptive events is its resilience, or the ability of the network to "bounce back" to a desired performance state. Building on the extensive reliability engineering literature on measuring component importance, or the extent to which individual network components contribute to network reliability, this paper provides two resilience-based component importance measures. The two measures quantify the (i) potential adverse impact on system resilience from a disruption affecting link i, and (ii) potential positive impact on system resilience when link i cannot be disrupted, respectively. The resilience-based component importance measures, and an algorithm to perform stochastic ordering of network components due to the uncertain nature of network disruptions, are illustrated with a 20 node, 30 link network example.