> for almost all cases, the minimum cut will be to pick a node and seperate it from the rest of the nodes. You're assuming that nodes have 1 or 2 edges coming

> for almost all cases, the minimum cut will be to pick a node and seperate it from the rest of the nodes. You're assuming that nodes have 1 or 2 edges coming out of them. If every node has up to (# nodes)-1 edges incident on it, then it's non-obvious which of the 2^(# node) subsets gives the min cut. It's definitely not justified to only consider the subsets with 1 nodes: what if you have 10 nodes: 5 blue and 5 yellow, and the blue ones are all connected to each other with extremely heavy edges, and similar for the yellow nodes, and there is one very light edge between the two regions? Then in this case, the min cut would be to separate blue from yellow (i.e. cut off a 5-node subset), _not_ 1 node. The general case of arbitrary nodes and edges will be somewhere in between what I have described and what you're thinking of, so a general algorithm that works for all cases is definitely not as trivial as just trying out every 1-node subset.