Recall that a flow network is a directed graph G$=($V$,$E$)$ with a source s$,$ a sink t$,$ and a capacity function c:V$\backslash$times V$->$R$\_(0)^(+)$that is positive on E and $0$ outside EG$,$s$,$t$,$c G$=($V$,$E$)$f$,$f$^(\text{'})$ are different if they are different as functions V$\backslash$times V$->$R$.$ That is$,$ if f$($u$,$v$)!=$f$^(\text{'})($u$,$v$)$ for some u$,$vinV. The number of maximum flows is at most the number of minimum cuts. The number of maximum flows is at least the number of minimum cuts. If the value of f is $0$ then f$($u$,$v$)=0$ for all u$,$v$.$ The number of maximum flows is $1$ or infinity. The number of minimum cuts is finite.