关键词: 网络最大流，割集，部分割，最小割

Abstract: Network maximum-flow problem is a classical module in graph theory. First, based on the rough set attribute reduction algorithm of discernibility matrix, it defines a partial cut set matrix. Afterwards, it finds out all the cut by meet and join operations for sets. Furthermore, the minimum cut is yielded out. At last, it gets the maximum flow of the network with the assistance of the theorem of maximum flow minimum cut.

Key words: Network maximum-flow, Cut set, Partial cut set, Minimum cut