Core Idea - Extracting the Cut Edges

After max flow, build the residual graph. Run BFS from $s = 1$ to find all reachable vertices $S$. All other vertices are in $T$. The reachability test identifies which side of the cut each vertex is on. For each edge $(u, v)$ in the original graph, if $u \in S$ and $v \in T$, include it in the minimum cut.

These are the roads to block. Count these edges to verify they match the max flow value. If they do not match, you have made an implementation error.