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:


 * $G$ is a simple digraph. That is, $A$ is antisymmetric.
 * $\forall x, y \in V: \left({ \{ x, y \} \in E \iff (x, y) \in A \lor (y, x) \in A }\right)$

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