Minimal Cuts up to Third Order in a Planar Graph

This paper presents a new algorithm to determine all minimal cuts up to third order that isolate some sink node from all source nodes in a planar graph. The algorithm has the advantage of having a linear complexity, which makes the problem tractable as opposed to path oriented methods, where path determination grows exponentially with the size of the graph. This algorithm can be used when the size of the graph requires computer assistance, and it can simplify the application to large systems, of reliability evaluation techniques based on minimal cuts. The limitation of cuts up to third order has a numerical reason since cuts of higher order often negligibly affect the system indexes. A computer application to a graph that models an urban power distribution network shows the algorithm´s capacity to handle complex problems and reduce CPU time.