Why it matters

Edmonds-Karp is guaranteed polynomial. Understanding shapes solid max flow implementations.

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The architecture

Ford-Fulkerson + BFS.

BFS finds shortest augmenting path (fewest edges).

Edmonds-Karp mechanicsBFS augmentshortest pathPush min capacityalong pathO(VE²)guaranteed polyShortest paths increase monotonically; each edge saturates O(V) times
Edmonds-Karp bound.
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How it works end to end

Analysis: at most O(VE) augmenting paths; each BFS is O(E). Total O(VE²).

Practical: often faster than worst case.

Alternatives: Dinic (O(V²E)), push-relabel (O(V²√E)).