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Minimum Spanning Tree Calculator

Work out minimum spanning tree instantly with clear inputs, formula shown and shareable results.

About Minimum Spanning Tree Calculator

Kruskal's algorithm sorts the edges by weight and adds each one that joins two different components, tracked with a union-find structure. A spanning tree on n vertices always has exactly n − 1 edges.

Formulas

Kruskal

sort edges ascending, add an edge whenever it connects two distinct components

Tree size

a spanning tree on n vertices has n − 1 edges

Worked example

With the default values below, Minimum Spanning Tree Calculator returns Total weight of the tree of 11.000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Edges as from,to,weight triples
1,2,4 1,3,2 2,3,1 2,4,5 3,4,8 4,5,3
Algorithmone of Kruskal (sort edges), Prim (grow from a vertex)
Kruskal (sort edges)

Results

Total weight of the tree
11.000000
Edges in the tree
2-3 (1), 1-3 (2), 4-5 (3), 2-4 (5)
Edges chosen
4
Connectivity
Spanning tree found, the graph is connected

Step by step

  1. 1Values used
  2. 2Kruskal
  3. 3Tree size
  4. 4Total weight of the tree= 11.000000
  5. 5Edges in the tree= 2-3 (1), 1-3 (2), 4-5 (3), 2-4 (5)
  6. 6Edges chosen= 4
  7. 7Connectivity= Spanning tree found, the graph is connected

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For the sample graph?

Edges 2-3 (1), 1-3 (2), 4-5 (3) and 2-4 (5) total 11 across five vertices.

Does Prim give the same weight?

Yes. Any correct algorithm finds a minimum total, though the specific edges can differ when weights tie.

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