Important: The networks package has been deprecated.  Use the superseding package GraphTheory instead.

This routine returns the maximum flow from s to t in G.  It is normally called by the routine flow() which performs some setup and preliminary analysis based on edge-connectivity calculations.

Edge weights of G are interpreted as capacities.

If a non-negative integer upper bound n is specified for the flow then the routine terminates after a flow of n in G is found even if greater flows are possible.

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

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

$G≔\mathrm{petersen}\left(\right)\:$

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

$3$

$\mathrm{eset}$

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

$\mathrm{comp}$

$\left\{1\right\}$

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

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

$1$

$\mathrm{eset}$

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