See here

Basic inequality:

Ford-Fulkerson algorithm: algorithm to find maximum flow using residual graph

• Can prove that using this algorithm you find a cut for which the inequality (1) is tight.
• As the inequality holds for all flows, and for all cuts, this should be the maximum flow and minimum cut

This is an example of using continuous optimization (maximum flow) to solve a discrete optimization problem (min cut).

For irrational capacities, the FF algo can lead to infinite number of iterations.

Chosing paths optimally

Dinits algorithm

Independent paths, connectivity, and cut sets