Problem - Network Segmentation

You are given an undirected graph with $n$ vertices and weighted edges. You want to partition vertices into two groups such that the total weight of edges crossing the partition is minimized. This is the global minimum cut problem. You need to find the cut with the smallest total edge weight, without fixing $s$ and $t$. Any partition is a candidate.

Unlike minimum $s$-$t$ cut where endpoints are given, you consider all possible partitions and find the one with minimum cost.