Question

Okay so here’s my algorithm for finding a Cut in a graph (I’m not talking about a min cut here)

Say we’re given an adjacency list of a non-directed graph.

1. Choose any vertice on the graph (let this be denoted by pivot)
2. Choose any other vertice on the graph (randomly). (denote this by x)
3. If the two vertices have an edge between them, then remove that edge from the graph. And dump all the vertices that x is connected to, onto pivot. (if not then go back to Step 2.
4. If any other vertices were connected to x, then change the adjacency list so that now x is replaced by pivot. Ie they’re connected to Pivot.
5. If number of vertices is greater than 2 (go back to step 2)
6. If equal to 2. Just count number of vertices present in adjacency list of either of the 2 points. This will give the cut

My question is, is this algorithm correct?

Answer 1

That is a nice explanation of Krager’s Min-Cut Algorithm for undirected graphs.

I think there might one detail you missed. Or perhaps I just mis-read your description.

You want to remove all self-loops.

For instance, after you remove a vertex and run through your algorithm, Vertex A may now have an edge that goes from Vertex A to Vertex A. This is called a self-loop. And they are generated frequently in process of contracting two vertices. As a first step, you can simply check the whole graph for self-loops, though there are some more sophisticated approaches.

Does that make sense?