Network Maximum Flow Calculator
Calculate directed source-to-sink maximum flow and a capacity-equal minimum cut from integer-capacity edges.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use Edmonds–Karp breadth-first augmenting paths with reverse residual edges and aggregate parallel capacities.
Augment source-to-sink residual paths; maximum flow equals the final source-side cut capacity
Worked example
The default four-node network carries maximum flow 5, equal to the capacities 3+2 leaving source zero.
Assumptions and input details
Whole nonnegative capacities up to 1e9 per edge, source/sink inside the node set. No lower bounds, costs, transit time, losses or multiple commodities. Cut membership concerns the aggregated directed graph.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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