Definition:Adjacent (Graph Theory)/Edges

Definition

Let $G = \struct {V, E}$ be an undirected graph.

Two edges $e_1, e_2 \in E$ of $G$ adjacent if and only if there exists a vertex $v \in V$ to which they are both incident.

Let $G = \struct {V, E}$ be a digraph.

Two arcs $e_1, e_2 \in E$ of $G$ adjacent if and only if there exists a vertex $v \in V$ to which they are both incident.

Let $G = \struct {V, E}$ be a graph.

Two edges $u, v \in V$ of $G$ are non-adjacent if and only if they are not adjacent.

Adjacent elements of a graph can also be described as neighboring (British English spelling: neighbouring).

Results about adjacency in the context of Graph Theory can be found here.