Definition:Orientation (Graph Theory)

Definition
Let $G = (V, E)$ be a simple graph.

Let $H = (V, A)$ be a directed graph.

Then $H$ is an orientation of $G$ iff both of the following hold:


 * For each element $\{ x, y \}$ of $E$, either $(x, y) \in A$ or $(y, x) \in A$ but not both.
 * For each element $(x, y)$ of $A$, $\{x, y\} \in E$.

Note that every simple digraph is an orientation of exactly one simple graph, but a simple graph may have more than one orientation.