Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For Engineers · Spanning Tree

Spanning Tree for a water network

Built for engineers using it for real design work. Go from concept to a running model in the browser, then scale to the cloud when needed. Simulate a water network live below — adjust the inputs and watch it respond, right in your browser.

Minimum Spanning TreeLive

Kruskal's algorithm

Controls

Presets

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.

▶ Run in Python

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.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

or unlock everything with Pro →

Also for:Students Researchers Educators Hobbyists & Makers K-12 Students First Responders General version →

More with Spanning Tree

Spanning Tree for a road network Spanning Tree for a social graph Spanning Tree for a subway map Spanning Tree for a supply network Spanning Tree for a flight network Spanning Tree for a power grid Spanning Tree for a computer network Spanning Tree for a citation graph

Frequently asked questions

Is this good for engineers?: Yes — this version of "Spanning Tree for a water network" is framed for engineers using it for real design work. Go from concept to a running model in the browser, then scale to the cloud when needed.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.