Network flow stems from our original Bipartite Matching problem. This problem can model situations where objects need to be matched and when we need collections of pairs. We could also look for the largest matching set.

A flow network is a graph where each edge has an non-negative capacity associated with it. The is one source node and one sink node and these follow the standard definitions. Flow must not be greater than the capacity of the edge it travels on and it must also be conserved, that is, flow into a node must equal the flow out of a node (except for the source and sink nodes).