Resilience Measure of Network Systems by Node and Edge Indicators

This paper explores and analyzes resilience measures in network systems from different perspectives, which is beneficial to maintain the function of the whole networks. Few papers study resilience by using intermediate indicators. They straightly correlate resilience with basic entities, ignoring the modularized impact. Furthermore, some literatures do not further explain how nodes and edges play different roles in affecting network resilience. In this paper, resilience measures are proposed from perspective of various network-related elements, including the node and edge indicators in the network system. Through analyzing the characteristics of nodes and edges during failure, the matrices of node resilience and edge resilience are structured. Then, by processing and iterating two types of matrices, the resilience of the entire network is measured. The effect of node resilience and edge resilience on the network system is discussed. Our results show that node-related and edge-related indicators are both suitable to measure local stability. Besides, nodes always have a greater influence on network resilience than edges. Finally, a numerical example is given to verify the rationality of the proposed measures.