Time Complexity

Edmonds-Karp runs in $O(VE^2)$ time. Here is why: Each BFS takes $O(V + E) = O(E)$ time. The number of augmenting paths is at most $O(VE)$, because each augmentation increases the distance from source to some node. Total: $O(VE) \times O(E) = O(VE^2)$. For sparse graphs ($E \approx V$), this is $O(V^3)$. For dense graphs ($E \approx V^2$), this is $O(V^5)$.

In practice, the algorithm often runs much faster than the worst-case bound.

Space complexity is $O(V + E)$ for the data structures used.