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For K-12 Students · Maximum Flow

Maximum Flow for a project timeline

Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a project timeline live below — adjust the inputs and watch it respond, right in your browser.

Maximum FlowLive

Edmonds-Karp network flow

Controls

Presets

Capacity S→A

Capacity B→D

The max-flow problem asks how much can be pushed from a source to a sink through a network of capacity-limited edges. Edmonds-Karp repeatedly finds an augmenting path and saturates it until none remain. By the max-flow min-cut theorem, the answer equals the capacity of the cheapest set of edges that, if cut, disconnects source from sink — the bottleneck.

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Data Inspector

Maximum flow18

Nodes6

Bottleneckmin cut

Governing equation

∣ f ∣ = v \sum f (s, v) = 18 = cut min c (S, T)

Reading this result: Both feed edges are generous, so the bottleneck has moved to the fixed interior capacities — adding more feed capacity no longer raises the max flow (min-cut theorem).

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Frequently asked questions

Is this good for k-12 students?: Yes — this version of "Maximum Flow for a project timeline" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.