How do I simulate a metro system?

Open this page and use the live Bipartite Matching tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.

Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.

Can I use my own numbers?

Absolutely — every input is adjustable, and with data import you can drive a metro system from your own measurements.

Use case · powered by Bipartite Matching

Bipartite Matching for a metro system

Simulate a metro system live in your browser. This runs the real Bipartite Matching solver — adjust the inputs, watch it respond instantly, and export the result. No install, no account.

For:Students Researchers Educators Engineers Hobbyists & Makers K-12 Students First Responders

Bipartite MatchingLive

assignment problem

Controls

Presets

Edge density

Maximum bipartite matching pairs items from two groups — workers to jobs, students to schools, organs to recipients — so that as many valid pairings as possible are made, with no one assigned twice. Kuhn's algorithm repeatedly finds augmenting paths that improve the matching. The green edges are the optimal assignment.

▶ Run in Python

Data Inspector

Matched pairs0

Max possible6

Methodaugmenting paths

Governing equation

∣ M ∣ = cover min ∣ C ∣ = 0 (K \overset{o}{¨} nig: max matching = min vertex cover)

Reading this result: Only 0 of 6 paired: at 40% density the graph is too sparse, so many workers have no eligible job and augmenting paths run out early.

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

or unlock everything with Pro →

About this simulation

The full Bipartite Matching tool models a metro system with the same numerics engineers and scientists use — running entirely client-side. Change any parameter and the result updates in real time, so you can build intuition, check a design, or teach the concept without spreadsheets or installs.

More you can do with Bipartite Matching

Bipartite Matching for a road network Bipartite Matching for a social graph Bipartite Matching for a subway map Bipartite Matching for a supply network Bipartite Matching for a flight network Bipartite Matching for a power grid Bipartite Matching for a computer network Bipartite Matching for a citation graph

Other ways to simulate a metro system

Shortest Path for a metro system Spanning Tree for a metro system Graph Coloring for a metro system Small-World Network for a metro system PageRank for a metro system Network Centrality for a metro system

Frequently asked questions

How do I simulate a metro system?: Open this page and use the live Bipartite Matching tool below — set your inputs and the simulation runs instantly in your browser using real numerics. No install, no account needed.
Is it free?: Yes. The simulation runs free in your browser. A one-time unlock or a Pro plan adds advanced parameters, saved presets, data import, and clean exports.
Can I use my own numbers?: Absolutely — every input is adjustable, and with data import you can drive a metro system from your own measurements.