figure graph (leftand its maximum flow combine and distribute flow in any manner that it likesas long as edge capacities are not violated and as long as flow conservation is maintained (what goes in must come outlooking at the graphwe see that has edges of capacities and leaving itand has edges of capacities and entering it so perhaps the maximum flow could be instead of howeverfigure shows how we can prove that the maximum flow is we cut the graph into two partsone part contains and some other verticesthe other part contains since flow must cross through the cutthe total capacity of all edges (uvwhere is in ' partition and is in ' partition is bound on the maximum flow these edges are (acand (dt)with total capacity so the maximum flow cannot exceed any graph has large number of cutsthe cut with minimum total capacity provides bound on the maximum flowand as it turns out (but it is not immediately obvious)the minimum cut capacity is exactly equal to the maximum flow figure cut in graph partitions the vertices with and in different groups the total edge cost across the cut is proving that flow of is maximum