# Definition:Adjacent (Graph Theory)/Edges

< Definition:Adjacent (Graph Theory)(Redirected from Definition:Adjacent Edges (Graph Theory))

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## Definition

### Undirected Graph

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.

### Digraph

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.

### Non-Adjacent

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.

## Also known as

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

## Also see

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

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**adjacent**:**1. b.**(of a pair of edges in a graph) - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**adjacent edges**