Definition:Incident (Graph Theory)

Undirected Graph
Let $G = \left({V, E}\right)$ be an undirected graph.

Let $u, v \in V$ be vertices of $G$.

Let $e = \left\{{u, v}\right\} \in E$ be an edge of $G$:


 * IncidentGraph.png

Then $e = \left\{{u, v}\right\}$ is incident to $u$ and $v$, or joins $u$ and $v$.

Similarly, $u$ and $v$ are incident to $e$.

Digraph
Let $G = \left({V, E}\right)$ be a digraph.

Let $u, v \in V$ be vertices of $G$.

Let $e = \left({u, v}\right)$ be an arc that is directed from $u$ to $v$:


 * IncidentDigraph.png

Then the following definitions are used:

Incident From

 * $e$ is incident from $u$;


 * $v$ is incident from $e$.

Incident To

 * $e$ is incident to $v$;


 * $u$ is incident to $e$.

Planar Graph
Let $G = \left({V, E}\right)$ be a planar graph.

Then a face of $G$ is incident to an edge if the edge is one of those which surrounds the face.

Similarly, a face of $G$ is incident to a vertex if the vertex is at the end of one of those incident edges.