 Flow network edge capacity

A directed edge capacity is the upper bound $c_{ij}\ge 0$ on the feasible nonnegative flow through that edge. In a residual network, its forward residual capacity is $c_{ij}-f_{ij}$ and its backward residual capacity is $f_{ij}$. Increasing every edge capacity need not increase the maximum flow by that same amount, because a cut of a flow network can contain several edges.