# Definition:Graph (Graph Theory)/Formal Definition

## Definition

A **graph** is an ordered pair $G = \left({V, E}\right)$ such that:

- $V$ is a set, called the vertex set;
- $E$ is a set of 2-element subsets of $V$, called the edge set.

That is: $E \subseteq \left\{{\left\{{u, v}\right\}: u, v \in V}\right\}$.

$E$ can also be described as an antireflexive, symmetric relation on $V$.

## Sources

- 1977: Gary Chartrand:
*Introductory Graph Theory*... (previous) ... (next): $\S 1.3$: Graphs