Definition:Relation/Relation as Ordered Pair

Definition
Some sources define a relation between $S$ and $T$ as an ordered pair:
 * $\left({S \times T, P \left({s, t}\right)}\right)$

where:
 * $S \times T$ is the Cartesian product of $S$ and $T$
 * $P \left({s, t}\right)$ is a propositional function on ordered pairs $\left({s, t}\right)$ of $S \times T$.

Such sources then define the graph of the relation as:
 * $\mathcal R = \left\{{\left({s, t}\right) \in S \times T: P \left({s, t}\right)}\right\}$

that is, the set of all $\left({s, t}\right)$ in $S \times T$ for which $P \left({s, t}\right)$ holds.

Hence the graph of a relation is simply what is defined on this page as a relation.

Whether there are any advantages to this form of treatment is debatable. In general, this website will not use this somewhat more elaborate terminology.