No. of edges in the path is of length atmost two . . If k is an intermediate vertex in path p , then we can break the path from i to j as shown in the figure. From here, we can define a recursive relation between k th iteration and previous iteration k-1. Based on the recursive relation the following algorithm is deviced. After analysis it is seen that there is no need to store matrices from time before k-1 when the current iteration is k.
Every edge is associated with a real flow value.
Source vertex is a vertex which has zero in-flow and flow anly comes out of the source. Sink vertex has a zero out-flow, flow is all absorbed in this vertex. For all u , v of V except the source and sink vertices, every thing that goes in must come out. In the maximum-flow problem , we are given a flow network G with source s and sink t , and we wish to find a flow of maximum value from s to t . This method is iterative.