Definition:Connected Relation

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.