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For Students · Spanning Tree

Spanning Tree for a road network

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a road network live below — adjust the inputs and watch it respond, right in your browser.

Minimum Spanning TreeLive

Kruskal's algorithm

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Nodes

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.

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Data Inspector

Nodes9

Tree edges8

Total weight0

Governing equation

W (T) = e \in T \sum w (e) = 0 (∣ T ∣ = 8 edges)

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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Frequently asked questions

Is this good for students?: Yes — this version of "Spanning Tree for a road network" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.