For Students · Maximum Flow
Maximum Flow for a pipeline layout
Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a pipeline layout live below — adjust the inputs and watch it respond, right in your browser.
Maximum FlowLive
Edmonds-Karp network flow
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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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Maximum flow18
Nodes6
Bottleneckmin cut
Governing equation
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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