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Network flow (max flow) calculator

Compute the maximum flow through a capacitated network. Enter directed arcs with capacities ("S -> A : 10"), a source and a sink, and the Edmonds-Karp algorithm returns the maximum flow value plus the flow on every arc, highlighting the saturated arcs that form the minimum cut (max-flow equals min-cut).

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Network flow (max flow) calculator is free to use as often as you like, directly from this page. It covers 10"), a source and a sink, and the Edmonds-Karp algorithm returns the maximum flow value plus the flow on every arc, highlighting the saturated arcs that form the minimum cut (max-flow equals min-cut) — adjust any of them and the result follows immediately.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What is Network flow (max flow) calculator?

Compute the maximum flow through a capacitated network. Enter directed arcs with capacities ("S -> A : 10"), a source and a sink, and the Edmonds-Karp algorithm returns the maximum flow value plus the flow on every arc, highlighting the saturated arcs that form the minimum cut (max-flow equals min-cut).

What does a concrete case look like?

S→A 10, A→T 5, S→B 4, B→T 8 → max = 9 — the tool shows every step in between, not just the final figure.

What does it take into account?

It factors in 10"), a source and a sink, and the Edmonds-Karp algorithm returns the maximum flow value plus the flow on every arc, highlighting the saturated arcs that form the minimum cut (max-flow equals min-cut). Change any of them and the output follows immediately.

When would I actually use this?

Anything modelled as points and connections: a shortest route, a network's capacity, a schedule with dependencies, or a circuit reduced to its logic.

What is the most common mistake?

Assuming a shortest path stays shortest when a weight changes sign. Negative edges break the greedy argument Dijkstra rests on, and the algorithm returns a confident wrong answer rather than an error.

What else is filed next to it?

Bitwise Calculator, Delaunay triangulation generator and Dijkstra shortest path calculator share its section. They are not variants of it — being filed together is not the same as being alike — but that is where to look if this turned out not to be the tool you wanted.

Where do the figures come from?

The algorithms are the textbook ones and their results are exact for the graph you enter. What varies is cost: several of these problems have no known efficient solution, so large inputs are answered by heuristic and the tool says when that is the case.

Further reading

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