Connect everything for the least cost. A minimum spanning tree links every node with no wasted edges and no loops — the cheapest possible backbone.
Minimum Spanning TreeLive
Kruskal's algorithm
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A minimum spanning tree connects every node with the least possible total edge weight and no cycles. Kruskal's algorithm sorts all edges and adds the cheapest that does not form a cycle, using a union-find structure to detect them. It designs efficient road, power, and network layouts that reach everywhere for the lowest cost.
Reading this result: A spanning tree over these 9 nodes always uses exactly 8 edges with no cycles — Kruskal keeps adding the cheapest edge that joins two separate groups until every node is connected.
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How it works
Kruskal's algorithm sorts every edge by weight and greedily adds the cheapest that does not create a cycle, using a union-find structure to detect cycles instantly. The result spans all nodes at minimum total cost. It designs efficient road, pipeline, power, and telecom networks, and underlies clustering algorithms.
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Is this minimum spanning tree Kruskal tool really free?▾
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The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.