Given flow network G and flow f, an **augmenting path** p is a simple path
from s to t in the residual network *G*_{f}.

The minimum net flow along path p in *G*_{f} indicates the amount flow can
increase along this path in G.

Thus, define the **residual capacity of path p** as

Define flow *f*_{p} in *G*_{f} as

Define **flow sum ***f*_{1}** + ***f*_{2} as
.