Definition:Connected Relation

Definition
Let $$\mathcal R \subseteq S \times S$$ be a relation on a set $$S$$.

Then $$\mathcal R$$ is defined as connected iff:
 * $$\forall \left({a, b}\right) \in \mathcal R: a \ne b \implies \left({a, b}\right) \in \mathcal R \or \left({b, a}\right) \in \mathcal R$$

That is, iff every pair of distinct elements is related (either or both ways round).

This can also be called a total relation but beware of confusing this with left-total and right-total relations, which mean something else altogether.