Definition:Graph (Graph Theory)/Formal Definition

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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 $V$.