A novel and fast algorithm for locating minimal cuts up to second order of undirected graphs with multiple sources and sinks

Among various methods of evaluating reliability of a system, those based on minimal cuts (MC) are more advantageous. Calculating reliability of a system is easier by means of MCs. In addition, MCs locate unreliable parts of a system and help the engineer to improve the reliability of the system. Many algorithms have been investigated to enumerate MCs of a network. In this paper, a new and fast algorithm is presented that can deal with any undirected graph with multiple sources and sinks (e.g. power transmission and distribution systems). By defining the new concept of minimal cycles of the graph, first and second order MCs can be easily searched. Our results show that the proposed algorithm can find MCs up to second order in any undirected graph through a fast process.