Definition:Orientation (Graph Theory)
Definition
Let $G = \left({V, E}\right)$ be a simple graph.
Let $H = \left({V, A}\right)$ be a directed graph.
Then $H$ is an orientation of $G$ if and only if both of the following hold:
- $G$ is a simple digraph. That is, $A$ is antisymmetric.
- $\forall x, y \in V: \left({ \left\{{x, y}\right\} \in E \iff \left({x, y}\right) \in A \lor \left({y, x}\right) \in A }\right)$
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Note that every simple digraph is an orientation of exactly one simple graph, but a simple graph may have more than one orientation.
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