Pseudocode - Edmonds-Karp

I'll show you Edmonds Karp. It uses breadth first search (BFS) to find an augmenting path in the residual graph. Each iteration pushes bottleneck flow.

function maxFlow(s, t):
    flow = 0
    while true:
        parent = bfs(s, t)
        if parent[t] is null:
            break
        add = INF
        v = t
        while v != s:
            u = parent[v]
            add = min(add, cap[u][v])
            v = u
        v = t
        while v != s:
            u = parent[v]
            cap[u][v] = cap[u][v] - add
            cap[v][u] = cap[v][u] + add
            v = u
        flow = flow + add
    return flow

BFS bounds the number of augmentations. The algorithm runs in $O(VE^2)$ time and uses $O(V + E)$ space.