Given a simple undirected connected graph $G$, I want to find a min-cut of $G$ using a randomized algorithm.
My attempt was to select a random edge in $G$ and reduce that edge to a single vertex. And recursively do it until the number of vertices is at most 2.
The number of edges present (in the resulting multi-graph) will be the min-cut. This is the standard algorithm I found at many places.
Will this lead to the exact number of min-cut and how can I extract the vertices on each side of the cut?