This problem shows how minimum cut models real scenarios. Blocking roads, cutting wires, or removing connections all reduce to finding minimum cuts. The abstraction is widely applicable. The bidirectional edge trick (two directed edges) is standard for undirected graphs in flow networks.
Remember to deduplicate when listing cut edges or you will report each road twice. Max flow gives you the cut size, but extracting the actual edges requires the residual graph. The reachability from determines which side of the cut each vertex belongs to.