Based on the directed graph of primary relay and backup relay's coordination relationships， a new method to determine the minimum break point set（MBPS） by graph simplification is proposed in this paper. The sequence and the principle of the directed graph simplification are given， and relays are classified according to the priority. The candidate break point is chosen from the higher priority category having the largest backup dependency degree， meanwhile the vertex of the self-loop obtained during contraction operation is selected as a break point. The presented method can be applied to solve the MBPS problem for the coordination of entire network or in the same zone.