---
tag: NJ13KN813B
kind: concept
name: Connected relation
aliases: [complete-relation, connex-logic, connex-mathematics, connex-relation, connexity, semi-connex-relation, semiconnex-relation, strongly-connected-relation, total-relation-order]
sources:
  - wikipedia: en:57495962@r1357323844
    locator: Connected relation
    note: adopted
    mention: wikipedia://en/57495962
    sections: [Summary]
same_as:
  wikidata: Q2481270
  wikipedia: Connected relation
inventory: [7YHBKPCQZV]
---

## Summary

In mathematics, a relation on a set is called **connected** or **complete** or **total** if it relates (or "compares") all distinct pairs of elements of the set in one direction or the other while it is called **strongly connected** if it relates all pairs of elements. As described in the terminology section below, the terminology for these properties is not uniform. This notion of "total" should not be confused with that of a total relation in the sense that for all $x \in X$ there is a $y \in X$ so that $x \mathrel{R} y$ (see serial relation).