A New Approach to Constructing A Minimum Edge Cut Set Based on Maximum Flow

The maximum flow algorithm has long been known for calculating the minimum edge cut of any two vertices of a connected graph. The original algorithm, however, does not tell us which edges should be taken exactly and therefore there could be more than one way to construct a minimum-edge-cut set. In this paper, we propose a new method to get a minimum-edge-cut set by selecting edges of a graph in the order of betweenness. By comparing with the augmenting path method, it tends to make the two divided parts of a graph more balanced.