Definition:Connected Relation

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

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

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

Also see

 * Total Relation: a connected relation which also insists that $\left({a, b}\right) \in \mathcal R \lor \left({b, a}\right) \in \mathcal R$ even for $a = b$
 * Trichotomy