IsNetwork('G','s','t') outputs true if the directed graph G is a network with s as the source and t as the sink, and false otherwise.

IsNetwork('G') tests if a directed graph is a network. The output is a sequence of two sets of vertices, sources and sinks, of all possible sources and sinks.  If these sets are both empty then G is implicitly not a network.

A network is a connected directed graph with at least one vertex with indegree 0 (the source) and at least one vertex with outdegree 0 (the sink). Note that under this definition a network may have an internal cycle.

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

$N≔\mathrm{Digraph}\left(\left\{\left[1\,2\right]\,\left[1\,3\right]\,\left[2\,4\right]\,\left[3\,4\right]\right\}\right)$

$N≔\mathrm{Graph\; 1:\; a\; directed\; graph\; with\; 4\; vertices\; and\; 4\; arc(s)}$

$\mathrm{IsNetwork}\left(N\right)$

$\left\{1\right\},\left\{4\right\}$

$\mathrm{IsNetwork}\left(N\,1\,4\right)$

$\mathrm{true}$

$\mathrm{IsNetwork}\left(N\,1\,2\right)$

$\mathrm{false}$

$\mathrm{DrawNetwork}\left(N\right)$