Как найти два элемента с максимальным количеством общих связей?

SELECT `t1`.`name`, `t2`.`name`, COUNT(*) AS `count`
  FROM `teacher` AS `t1`
  JOIN (
    SELECT DISTINCT `teacher_id`, `student_id`
      FROM `teacher_student` 
  ) AS `s1` ON `s`.`teacher_id` = `t1`.`id`
  JOIN (
    SELECT DISTINCT `teacher_id`, `student_id`
      FROM `teacher_student` 
  ) AS `s2` ON `s2`.`student_id` = `s1`.`student_id` AND `s2`.`teacher_id` > `s1`.`teacher_id`
  JOIN `teacher` AS `t2` ON `t2`.`id` = `s2`.`teacher_id`
  GROUP BY `t1`.`id`, `t2`.`id`
  ORDER BY `count`
  LIMIT 1