# Unique min-cut means unique max flow?

This is not a home work question.

Is that correct to say in a flow network, if min cut is unique then max flow must also be unique?

Assume we have two max flow in a network. Then for each max flow, we can get a min cut and they are surely different.

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The theorem states that the value of the sum of edge weights in a minimum $s$-$t$ cut of a graph is equal to the value of the maximum $s$-$t$ flow in the graph interpreted as a flow network. It does not establish a one-to-one correspondence between flows and cuts.
$1$-$5$ max-flow/min-cut is equal to one. While there is a single minimum cut ({1 - 2}). There are a lot of possible maximum flows (take the unit of flow entering 2 and distribute it between 3 and 4 as you like).