Randomized k-cut

Splits an undirected graph into k groups by merging the ends of random edges until k groups are left, and cuts the edges between them.

Time complexity O(V·E), gograph function partition.RandomizedKCut.

gograph picks the edges to contract at random, so the cut can change each time the server restarts.

Friend groups

Twelve friends in three circles: a climbing group, a book club and a band. Each edge joins two friends. Eli climbs and reads, and Hana reads and plays in the band, so each of them links two circles.

An undirected graph with 12 vertices and 21 edges.

Split the twelve friends into 3 groups and try to cut as few friendships as possible.

Use it in Go

cut, err := partition.RandomizedKCut(g, 3)
if err != nil {
	return err
}
for _, group := range cut.Supernodes {
	var members []string
	for _, v := range group {
		members = append(members, v.Label())
	}
	fmt.Println(members)
}
for _, e := range cut.CutEdges {
	fmt.Println(e.Source().Label(), e.Destination().Label())
}

Example graphs

• Friend groups, 12 vertices and 21 edges
• Office network, 13 vertices and 16 edges
• Maze, 30 vertices and 31 edges
• Karate club, 34 vertices and 78 edges

More in Partitioning

• Maximal cliques: Finds every group of vertices that are all adjacent to each other and can't take one more vertex.
• Girvan-Newman: Splits an undirected graph into k communities by removing, one at a time, the edge that the most shortest paths cross.

All algorithms