Important: The networks package has been deprecated.  Use the superseding command GraphTheory[MaxFlow] instead.

It returns the maximum flow from s to t in G.

If 'maxflow' option is set then flow of at most n in G is found.

This routine is normally loaded via the command with(networks) but may also be referenced using the full name networks[flow](...).

$\mathrm{with}\left(\mathrm{networks}\right)\:$

$G≔\mathrm{petersen}\left(\right)\:$

$\mathrm{flow}\left(G\,1\,2\,\mathrm{eset}\,\mathrm{comp}\right)$

$3$

$\mathrm{eset}$

$\left\{\left\{1\,2\right\}\,\left\{1\,5\right\}\,\left\{1\,6\right\}\,\left\{2\,3\right\}\,\left\{2\,8\right\}\,\left\{3\,4\right\}\,\left\{4\,7\right\}\,\left\{5\,9\right\}\,\left\{6\,7\right\}\,\left\{8\,9\right\}\right\}$

$\mathrm{comp}$

$\left\{1\,2\,4\,5\,6\,7\,8\,9\right\}$

$\mathrm{eset}≔'\mathrm{eset}'\:$$\mathrm{comp}≔'\mathrm{comp}'\:$

$\mathrm{flow}\left(G\,1\,5\,\mathrm{eset}\,\mathrm{comp}\,\mathrm{maxflow}=1\right)$

$1$

$\mathrm{eset}$

$\left\{\left\{1\,5\right\}\right\}$