# Definition:Graph (Graph Theory)/Edge

## Definition

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

The edges are the elements of $E$.

### Join

Let $u$ and $v$ be vertices of $G$.

Let $e = u v$ be an edge of $G$.

Then $e$ joins the vertices $u$ and $v$.

## Notation

If $e \in E$ is an edge joining the vertex $u$ to the vertex $v$, it is denoted $u v$.

## Endvertex

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

Let $e = u v$ be an edge of $G$, that is, $e \in E$.

The endvertices of $e$ are the vertices $u$ and $v$.

## Also see

When $G$ is a digraph, the edges are usually called arcs.