The MaxFlow command returns the optimal value for the max flow problem along with an optimal flow (as a Matrix).

The algorithm used is the Push-Relabel (Push-Preflow) algorithm of Goldberg et al. (see Introduction to Algorithms, Cormen, Leiserson, Rivest, 2nd edition). The complexity is  where n=|V| is the number of vertices of G and m=|E| is the number of edges.