Query to group fully recursive relationships in many-to-many junction table - sql

Question

Apologies if this is a duplicate somewhere, searching here and the web seems to have similar but not exact matches to my problem so I decided to post.
I'm calling this a fully recursive grouping in a many-to-many relationship. I have tried writing joins and ctes to do this but without full recursion I'm only getting one level deep, and I'm not exactly thrilled about trying to write nested dynamic cursors.
Assume expressions can be derived from this "junction" table to find distinct students / classes, therefore the question can be summarized by using only one set.
SELECT * FROM student_class
+-------------+----------+--------------+
| student_id | class_id | group_number |
+-------------+----------+--------------+
| 1 | A | null |
| 1 | C | null |
| 2 | A | null |
| 2 | B | null |
| 2 | C | null |
| 3 | E | null |
| 4 | B | null |
| 4 | F | null |
+-------------+----------+--------------+
The question is how to populate a group number through a recursive relationship for each student and for each class. Ex: if student_id 1 has class_id A, then what other students have class_id A? For those other students, what other classes do they have? For each of those other classes, which other students have those classes? Then keep recursing through results until no more dependencies are found.
So in this example the final update would only contain two groups, read like this since no other students have class_id C and student_id 3 has no other classes:
+-------------+----------+--------------+
| student_id | class_id | group_number |
+-------------+----------+--------------+
| 1 | A | 1 |
| 1 | C | 1 |
| 2 | A | 1 |
| 2 | B | 1 |
| 2 | C | 1 |
| 3 | E | 2 |
| 4 | B | 1 |
| 4 | F | 1 |
+-------------+----------+--------------+

Answer 1

This is really tricky. It is a graph walking algorithm (which is not that hard). But you have to define the graph. You can define a link between two classes by using a self join. That can then be used for a recursive CTE.
So, to get equivalences classes (kind of punny here), you can do:
with cs as (
select *
from (values (1, 'A'), (1, 'C'), (2, 'A'), (2, 'B'), (2, 'C'), (3, 'E'), (4, 'B'), (4, 'F')) v(student, class)
),
cc as (
select distinct cs1.class as class1, cs2.class as class2
from cs cs1 join
cs cs2
on cs1.student = cs2.student
),
cte as (
select cc.class1 as class, cc.class2 as grp, cast(',' + cc.class1 + ',' as varchar(max)) as grps
from cc
union all
select cte.class, cc.class2,
cast(grps + cc.class2 + ',' as varchar(max)) as grps
from cte join
cc
on cc.class1 = cte.grp and cte.grps not like '%,' + cc.class1 + ',%'
)
select cte.class, min(cte.grp)
from cte
group by cte.class;
If you want to convert them to numbers:
select cte.class, min(cte.grp),
dense_rank() over (order by min(cte_grp)) as group_number
from cte
group by cte.class;