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

• The paper introduces a new and fast algorithm for locating minimal cuts (MC).
• It is applicable for undirected graphs to find up to second order MCs.
• It is efficient for large scale networks containing multiple sources and sinks.
• It also has a linear time complexity related to the number of network edges.
• It can be used for evaluating and optimizing reliability of large scale networks.

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.