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.

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.