What is the standard maximum flow problem?
Given a directed graph in which every edge has a certain capacity c, a starting node known as the source, and an ending node known as the sink. We are asked to find another value, f, satisfying f < c for each edge such that for every node other than the source and sink, the sum of the values associated with the edges that enter the node must equal the sum of the values leaving the node. We call f the flow along that edge. We are asked to maximize the sum of the values associated with the edges leaving the source, which is the total flow in the network.