SQL Server 2017

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create table YourTable (
 ID int primary key identity(1,1), 
 A varchar(3),  
 B varchar(3), 
 C varchar(3), 
 X int); 
insert into YourTable (A, B, C) values
('A1', 'B3', 'C1'),
('A1', 'B2', 'C5'),
('A1', 'B10', 'C10'),
('A2', 'B1', 'C5'),
('A2', 'B8', 'C1'),
('A3', 'B1', 'C4'),
('A4', 'B6', 'C3'),
('A4', 'B3', 'C5'),
('A5', 'B7', 'C2'),
('A6', 'B10', 'C3'),
('A8', 'B5', 'C4');
11 rows affected

DECLARE @CurrentClusterID INT = 1;
DECLARE @UpdateCount INT = 1;
DECLARE @TopUnclusteredID INT = (SELECT TOP 1 ID FROM YourTable WHERE X IS NULL);

UPDATE YourTable SET X = @CurrentClusterID WHERE ID = @TopUnclusteredID;

WHILE @UpdateCount > 0
BEGIN
	UPDATE t
	SET t.X = @CurrentClusterID
	FROM YourTable t
	WHERE t.X IS NULL
		AND EXISTS (
		  SELECT 1 FROM YourTable d 
		  WHERE d.X =  @CurrentClusterID
			AND (d.A = t.A OR d.B = t.B OR d.C = t.C)
	  );
	  SET @UpdateCount = @@ROWCOUNT;
END;

SET @CurrentClusterID = @CurrentClusterID + 1;
SET @TopUnclusteredID = (SELECT TOP 1 ID FROM YourTable WHERE X IS NULL);

UPDATE YourTable SET X = @CurrentClusterID WHERE ID = @TopUnclusteredID;
SET @UpdateCount = 1;

WHILE @UpdateCount > 0
BEGIN
	UPDATE t
	SET t.X = @CurrentClusterID
	FROM YourTable t
	WHERE t.X IS NULL
		AND EXISTS (
		  SELECT 1 FROM YourTable d 
		  WHERE d.X =  @CurrentClusterID
			AND (d.A = t.A OR d.B = t.B OR d.C = t.C)
	  );
	  SET @UpdateCount = @@ROWCOUNT;
END;
11 rows affected

select * from YourTable order by ID;


ID
A
B
C
X


1
A1
B3
C1
1

2
A1
B2
C5
1

3
A1
B10
C10
1

4
A2
B1
C5
1

5
A2
B8
C1
1

6
A3
B1
C4
1

7
A4
B6
C3
1

8
A4
B3
C5
1

9
A5
B7
C2
2

10
A6
B10
C3
1

11
A8
B5
C4
1

ID	A	B	C	X
1	A1	B3	C1	1
2	A1	B2	C5	1
3	A1	B10	C10	1
4	A2	B1	C5	1
5	A2	B8	C1	1
6	A3	B1	C4	1
7	A4	B6	C3	1
8	A4	B3	C5	1
9	A5	B7	C2	2
10	A6	B10	C3	1
11	A8	B5	C4	1

ID	A	B	C	X
1	A1	B3	C1	1
2	A1	B2	C5	1
3	A1	B10	C10	1
4	A2	B1	C5	1
5	A2	B8	C1	1
6	A3	B1	C4	1
7	A4	B6	C3	1
8	A4	B3	C5	1
9	A5	B7	C2	2
10	A6	B10	C3	1
11	A8	B5	C4	1

ID	A	B	C	X
1	A1	B3	C1	1
2	A1	B2	C5	1
3	A1	B10	C10	1
4	A2	B1	C5	1
5	A2	B8	C1	1
6	A3	B1	C4	1
7	A4	B6	C3	1
8	A4	B3	C5	1
9	A5	B7	C2	2
10	A6	B10	C3	1
11	A8	B5	C4	1