Eulerian Graph

graph-theory

Definition

Eulerian Graph

A directed weakly connected graph $G=(V,E)$ is called Eulerian if and only if for all edges, the out degree and in-degree are equal:

$$\forall v\in V:d^{+}(v)=d^{-}(v)$$

Criteria

A undirected connected graph is Eulerian if all vertices have an even degree.

Conversely, a undirected connected graph is Eulerian if the graph has exactly two vertices with odd degree.