A network is a collection of nodes and arcs.
Flow enters and leaves at the nodes and passes through the
arcs. Generally there are lower and upper bounds on arc flows.
Each arc has a unit cost and the arc cost is the flow multiplied
by the unit cost. The goal is to find the flow that minimizes
Each arc has a gain factor that multiplies the
flow entering the arc to obtain the flow that leaves the arc.
A network with all gains equal to 1 is called a pure network.
If some gains are other than 1, the network is called a generalized