About the Edmonds Karp Algorithm
The Edmonds Karp algorithm solves a maximum flow problem. It finds the greatest possible flow from one source node to one sink node. Each directed edge has a capacity. Flow cannot exceed that capacity. The method is based on Ford Fulkerson. Its special rule is simple. It always chooses the shortest augmenting path by using breadth first search.
Why the Method Is Useful
This rule makes the process predictable. It avoids the random behavior found in some path choices. Each iteration explores the residual network. The residual network shows where more flow can still move. It also shows where earlier flow can be reversed. The calculator lists every path, bottleneck, and cumulative flow value. This helps students follow the method step by step.
How the Calculator Helps
Manual work can become long when a graph has many edges. A single missed residual update can change the final answer. This tool reduces that risk. Enter edges as from node, to node, and capacity. Then choose the source and sink. The result shows maximum flow, final edge usage, residual values, and a minimum cut. These outputs give a complete network view.
Interpreting the Result
The maximum flow is the total amount leaving the source. It also equals the total amount entering the sink. The minimum cut confirms the same value when the solution is optimal. Edges crossing from reachable nodes to unreachable nodes form that cut. Their combined capacity matches the maximum flow.
Study and Planning Use
This calculator is useful for maths practice, operations research, logistics, routing, and network design examples. It can model pipes, roads, data links, task assignment limits, or supply paths. The CSV report supports spreadsheet review. The PDF report is helpful for notes and class submissions.
Input Tips
Good input matters. Keep node names consistent. Avoid hidden spaces. Use one directed edge per row. Parallel edges are allowed. The calculator combines them into one capacity. Zero capacity edges are ignored by the search, yet they can still explain a model. Decimal capacities are accepted for learning examples. For formal integer network problems, use whole numbers. Always check whether the source and sink are named exactly as entered. Review unusual results before using them formally.