<div>This paper proposes a new resilience-based component importance ranking measure for multi-state networks from the perspective of a post-disaster restoration process. Considering the stochastic nature of disruptive events, the importance measure of each component is evaluated by finding the minimal recovery paths for various disruptive events, and it can be represented by a probability distribution.</div><div><br></div><div>The paper introduces a novel resilience-based component importance ranking measure for multi-state networks from the perspective of a post-disaster restoration process. Considering the stochastic nature of disruptive events, the importance measure of each component is evaluated by finding the minimal recovery paths for various disruptive events, and it can be represented by a probability distribution.</div><div><br></div><div>This paper takes inspiration from the resilience community literature, which has established a number of measures for component importance. Using these measures as building blocks, this paper proposes a resilience-based component importance ranking measure for multi-state networks from the perspective of post-disaster restoration processes. The proposed measure evaluates each component by finding the minimal recovery paths for various disruptive events, and it can be represented by a probability distribution.</div><div><br></div><div>The resilience of a network has always been a key factor in the Internet community. Inspired by the concept of component importance ranking used widely in reliability community, we derive a minimum set of indicators to assess network component importance. It considers both disruptive events and its recovery paths, allowing us to evaluate the importance of each component through finding minimal recovery path sequences for various disruptive events. By using this approach, we show that it yields better results than previous approaches used across several networks.</div><div><br></div><div>This paper is concerned with evaluating resilience using multi-state networks. The resilience of a multi-state network is defined as its ability to timely recover the maximum flow capacity to an acceptable level. This study considers developing a new resilience based component importance measure for network components, by quantifying their importance in terms of both capability and recovery time in the event of disruptions. In this work, we developed a connection space model for assessing network roles, which is capable of grouping nodes and links into different groups depending on their required capacities in order to ensure smooth operation of the entire network as well as preventing system downtime during an outage.<br></div>