The Stoer-Wagner algorithm finds the global minimum cut in O(n3) time. It works by repeatedly finding minimum s-t cuts for carefully chosen s and t, then merging vertices. The algorithm contracts the graph by merging vertices and tracking cut weights.
After n−1 iterations, you have checked enough cuts to find the global minimum. This is the standard approach for global minimum cut in undirected graphs.
Space complexity is O(V+E) for the data structures used.