Global Minimum Cut

A global minimum cut is the cut with the smallest capacity among all possible cuts, without specifying $s$ and $t$. You are not given fixed endpoints. You are looking for the cut that partitions the graph into two parts with the fewest total edges (or smallest total weight) crossing.

This cut represents the graph's overall vulnerability. This is harder than minimum $s$-$t$ cut because you need to check all possible pairs of sets. Without fixed endpoints, the search space is larger.