[SQL] Matching for 2 columns but matching all alternatives recuringly in SQL

My data look like this

Col_X Col_Y
a b
b c
c d
d e
f g
t y
y r
q w
n m
m k
m z

My final goal cluster table should be exactly like this:

Cluster
abcde
fg
nmkz
qw
tyr​

My pseudo data

select 'a' as x, 'b' as y union all
select 'b' as x, 'c' as y union all
select 'c' as x, 'd' as y union all
select 'd' as x, 'e' as y union all
select 'f' as x, 'g' as y union all
select 't' as x, 'y' as y union all
select 'y' as x, 'r' as y union all
select 'q' as x, 'w' as y union all
select 'n' as x, 'm' as y union all
select 'm' as x, 'k' as y union all
select 'm' as x, 'z' as y

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