Cut Capacity

The capacity of a cut $(S, T)$ is the sum of capacities of all edges going from $S$ to $T$. Edges from $T$ to $S$ do not count in a directed graph. Direction matters. For an undirected graph, you count each crossing edge once, regardless of direction.

For a directed graph, only edges leaving $S$ and entering $T$ contribute to the capacity. The capacity measures how much flow you need to block to disconnect $S$ from $T$. If you saturate all edges crossing the cut, no more flow can pass through.