How to link the pairs of values from 2 columns

I have a table [tt] with 2 columns which has a set of values that can repeat.
Columns are named [a] and [b]:

[a] [b]
1   2
1   3
1   4
2   1
2   3
3   2
4   1
4   5
5   4
5   6

I know how to query only the pairs:

SELECT t1.A, t1.B
    FROM tt AS t1
INNER JOIN tt AS t2
    ON t1.A = t2.B AND t1.B = t2.A

But how can I link the pairs together with adding a new column [pair_id] f.e. like this:

[a] [b] [pair_id]
1   2   1
2   1   1
1   4   2
4   1   2
2   3   3
3   2   3
4   5   4
5   4   4

Thank you!

>Solution :

Try the dense_rank function ordered by least and greatest functions.

select a, b,
  dense_rank() over (order by least(a, b), greatest(a, b)) pair_id
from tbl

Demo