Core Idea - Try All Pairs

One approach: for each pair of vertices $(s, t)$, compute the minimum $s$-$t$ cut. The global minimum cut is the smallest among all these cuts. This is conceptually simple. There are $O(n^2)$ pairs, and each min cut takes $O(n \cdot m)$ time with max flow.

Total time: $O(n^3 \cdot m)$, which is too slow for large graphs with thousands of vertices. You need a smarter algorithm like Stoer-Wagner that avoids checking all pairs explicitly.