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.