State the Max-flow min cut theorem for network flow analysis. Trace the execution of Ford-Fulkerson algorithm for finding the maximum flow in the graph.

Max-flow min cut theorem for network flow analysis:

If f is a flow in a flow network G(V,E) with source s and sink t, then the following conditions are equivalent:

• f is a maximum flow in G.

• the residual network G_f contains no augmenting paths.

• lfl=C(S,T) for some cut (S,T) of G.