Handling Bidirectional Roads

Since roads are bidirectional, represent each road as two directed edges: one from $u$ to $v$ and one from $v$ to $u$, both with capacity $1$. This is standard for flow networks. When you block a road, you block both directions. In the cut, you might see $(u, v)$ from $S$ to $T$ or $(v, u)$ from $S$ to $T$, but they represent the same physical road.

When listing cut edges, make sure you do not count the same road twice. Use the original edge list to avoid duplicates.