Eulerian digraphs

A digraph is Eulerian if there is a closed walk containing all vertices and edges, each edge exactly once. The following theorem gives a nice characterization of Eulerian digraphs, analogously to the Eulerian undirected graphs. The proof is very similar to the undirected case, so it is left as an exercise.

Exercise 27

Let be a digraph. Then, is Eulerian if and only if is weakly connected and for all .