 Widest augmenting path

An augmenting path maximizing the possible increase in flow, namely its smallest residual network edge capacity. If the remaining maximum flow is $F>0$ and the original undirected network has $m$ edges, a path has bottleneck at least $F/m$. Otherwise the vertices reachable through arcs of capacity at least $F/m$ define a cut of capacity strictly less than $F$, contradicting the max-flow min-cut theorem. Only one directed arc per original crossing edge contributes to that cut.