\begin{definition}[Definition:Connected Relation]
Let $\RR \subseteq S \times S$ be a relation on a set $S$.
Then $\RR$ is '''connected''' {{iff}}:
:$\forall a, b \in S: a \ne b \implies \tuple {a, b} \in \RR \lor \tuple {b, a} \in \RR$
That is, {{iff}} every pair of distinct elements is related (either or both ways round).
\end{definition}