Postgres 10

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create table YourTable (
 id int, 
 group_id int, 
 component_id int
);
insert into YourTable (id, group_id, component_id) values
  (1, 3, 123) 
, (2, 3, 456) 
, (3, 4, 123) 
, (4, 4, 456) 
, (5, 5, 123)
--, (5, 5, 789) 
--, (6, 3, 789)
5 rows affected

WITH RECURSIVE RCTE AS (
    SELECT id, group_id, component_id
    , 1 as Lvl
    , array[group_id] as group_ids
    , array[component_id] as component_ids
    FROM YourTable
    WHERE group_id IN (
      SELECT group_id
      FROM YourTable
      GROUP BY group_id
      HAVING COUNT(*) = 1
    )
    UNION ALL
    SELECT t.id, t.group_id, t.component_id
    , Lvl+1
    , cte.group_ids || t.group_id
    , cte.component_ids || t.component_id
    FROM RCTE cte
    JOIN YourTable t 
      ON t.group_id != ALL(group_ids)
     AND t.component_id != ALL(component_ids)
)
, CTE_ARRAYS AS (
    SELECT group_ids, component_ids
    FROM RCTE
    ORDER BY array_length(group_ids, 1) desc, Lvl desc
    LIMIT 1
) 
SELECT a.group_id, a.component_id
FROM CTE_ARRAYS c
CROSS JOIN LATERAL UNNEST(c.group_ids, c.component_ids) WITH ORDINALITY AS a(group_id, component_id)
ORDER BY a.group_id;


group_id
component_id


3
456

5
123