Definition:Adjacent (Graph Theory)

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

Two vertices $$u, v \in V$$ of $$G$$are said to be adjacent or neighboring if there exists an edge $$e = \left\{{u, v}\right\} \in E$$ of $$G$$ to which they are both incident.

Otherwise they are non-adjacent.

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

Two vertices $$u, v \in V$$ of $$G$$are said to be adjacent or neighboring if there exists an arc $$e = \left({u, v}\right) \in E$$ of $$G$$ to which they are both incident.

Otherwise they are non-adjacent.