Find all possible pairs based on transitivity via T-SQL - sql

Question

I have a concern that doesn't let me go for already several days.
The collective mind is the last resort I may rely on.
Assume we have a table with two columns. Actually, the values are GUIDs, but for the sake of simplicity let's take them as letters.
| a | b |
|---|---|
| x | y |
| y | x |
| y | z |
| z | y |
| m | n |
| m | z |
I need to create a T-SQL query that will present all the possible pairs out of trasitivity, i.e. if x=y, y=z, then x=z. Also, simmetry has to be there, i.e. if there is x=y, then there should be y=x as well.
In this particular case, I believe there is "full house", meaning that every letter is connected to all others through the intermediates. But I need a query that will show that.
All I did is here (SQLFiddle fails to run it):
WITH
t AS
(SELECT 'x' AS a, 'y' AS b
UNION ALL
SELECT 'y' AS a, 'x' AS b
UNION ALL
SELECT 'y' AS a, 'z' AS b
UNION ALL
SELECT 'z' AS a, 'y' AS b
UNION ALL
SELECT 'm' AS a, 'n' AS b
UNION ALL
SELECT 'm' AS a, 'z' AS b),
coupled_reflective AS --for reflective couples we take either of them
(SELECT t2.a, t2.b
FROM t t1
JOIN t t2 ON t1.a=t2.b
AND t1.b!=t2.a),
reversive_coupled_reflective AS --that's another half of the above couples (reversed)
(SELECT t2.b, t2.a
FROM t t1
JOIN t t2 ON t1.a=t2.b
AND t1.b!=t2.a),
rs AS -- reduce the initial set (t)
(SELECT *
FROM coupled_reflective
UNION
SELECT *
FROM t
EXCEPT
SELECT *
FROM reversive_coupled_reflective),
cte AS -- recursively iterate through the set to find transitive values (get linked by the left field)
(SELECT a, b
FROM rs
UNION ALL
SELECT rs.b, cte.b
FROM rs
JOIN cte ON rs.a=cte.a
AND rs.b!=cte.b),
cte2 AS -- recursively iterate through the set to find transitive values (get linked by the right field)
(SELECT a, b
FROM rs
UNION ALL
SELECT rs.a, cte.a
FROM rs
JOIN cte ON rs.b=cte.b
AND rs.a!=cte.a)
SELECT a, b FROM cte2
UNION
SELECT a, b FROM cte
UNION
SELECT a, b FROM t
UNION
SELECT b, a FROM t
But that doesn't do the trick, unfortunately.
The desired result should be
| a | b |
|---|---|
| x | y |
| y | x |
| y | z |
| z | y |
| m | n |
| m | z |
| n | m |
| z | m |
| x | z |
| z | x |
| x | m |
| m | x |
| x | n |
| n | x |
| y | m |
| m | y |
| y | n |
| n | y |
Is there a SQL-gifted buddy out there who can help me here, please?
Thanks.

Answer 1

You can use recursive CTEs, but you need a list of already visited nodes. You can implement that using a string:
with cte as (
select a, b, cast('{' + a + '}{' + b + '}' as varchar(max)) as visited
from t
union all
select cte.a, t.b,
(visited + '{' + t.b + '}')
from cte join
t
on cte.b = t.a
where cte.visited not like '%{' + t.b + '}%'
)
select distinct a, b
from cte;
Note:
The above follows the directed links in the graph. If you want undirected links, then include both:
with t as (
select a, b from yourtable
union
select b, a from yourtable
),
The rest of the logic follows using t.