The routing algorithm inside every GPS. Dijkstra's method finds the cheapest path through a weighted network, one nearest node at a time.
Shortest Path (Dijkstra)Live
weighted graph search
Controls
Dijkstra's algorithm finds the shortest path from a source (A, blue) to every other node in a weighted graph, always expanding the closest unvisited node next. The number inside each node is its shortest distance from A; the green edges trace the optimal route to your chosen destination. It powers GPS routing, network protocols, and logistics. Click any node to re-target.
Size a graph for the exportable Python solver below — the diagram stays a fixed six-node example.
Reading this result: Dijkstra grows a set of finalized nodes, each step expanding the nearest unvisited one and relaxing its outgoing edges. Because all weights are non-negative, the first time a node is finalized its distance is already optimal. This configuration describes 6 nodes and about 9 weighted edges (density 60%).
Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.
★ Sign in to save this setupSave your tuned setup, or drop this simulation into your own site, docs, or course page.
How it works
Dijkstra's algorithm computes the shortest distance from a source to every other node in a graph with non-negative edge weights, always finalizing the closest unvisited node next. It underlies GPS navigation, internet routing protocols, and logistics planning. The distances label each node and the highlighted edges trace the optimal route.
✦
Ask the AI about this model
The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
Yes. Shortest Path (Dijkstra) runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?▾
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?▾
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?▾
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.