Faster Algorithms

Edmonds-Karp is not the fastest. Dinic's algorithm runs in $O(V^2 E)$ time. Push-relabel algorithms can achieve $O(V^3)$ or better. For competitive programming, Edmonds-Karp is usually fast enough unless $V$ and $E$ are huge (over $10$,$000$).

Dinic's is faster but more complex to code. If time limits are tight, consider Dinic's. Otherwise, stick with Edmonds-Karp. It is simpler and less bug-prone. Know when the extra complexity is worth it.

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