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 $G$ be a digraph. Then, $G$ is Eulerian if and only if $G$ is weakly connected and $\deg^+(v) = \deg^-(v)$ for all $v \in V$.