Question: I need to find the minimum cut on a graph. I've been reading about flow networks, but all I can find are maximum flow algorithms such as Ford-Fulkerson, push-relabel, etc. Given the max flow-min cut theorem, is it possible to use one of those algorithms to find the minimum cut on a graph using a maximum flow algorithm? How?

The best information I have found so far is that if I find "saturated" edges i.e. edges where flow equals capacity, those edges correspond to the minimum cut. Is that true? It doesn't sound 100% right to me. It is true that all edges on the minimum cut will be saturated, but I believe there might also be saturated edges which are out of the minimum cut "path".

Answer: 
So, to give the exact procedure how to obtain the minimum cut:

1. Run Ford-Fulkerson algorithm to find the max flow and to get the residual graph1.
2. Run BFS **on the residual graph** to find the set of vertices that are reachable from source in the residual graph (respecting that you can't use edges with 0 capacity in the residual graph).
IMPORTANT: You have to use reverse edges in the residual graph to find the correct set of reachable vertices!!! [(See this algorithm)](http://www.geeksforgeeks.org/minimum-cut-in-a-directed-graph/ "algorithm")
3. All edges **in the original graph** which are from a reachable vertex to non-reachable vertex are minimum cut edges. Print all such edges.

1 Graph in which the capacity of an edge is defined like it's original capacity minus its flow (flow from the maximum flow network).
I think this is what other people are saying, but I found it unclear so here's my explanation:

From the source node, do a flood fill of the graph, travelling only along edges with residual capacity, marking each visited vertex. You can use a DFS for this. Recall that back edges from a vertex have a residual capacity - equal to the flow along the forward edge (ie. r(u, v) = remaining capacity for edge (u, v), r(v, u) = flow(u, v)).

In effect, this determines the S part of the S-T cut of the graph.

The minimum cut will now be the set of edges such that one vertex is marked from your flood fill above, and the other vertex is not marked. These will be edges without residual capacity (otherwise you would have traversed them in your DFS), and together form the minimum cut.

After removing these edges, the set of unmarked vertices will form the T section of the cut.