Find the genres that have at least 2 same directors, then print common genres and director id?

The dataset is like this:

g1 = {d1,d3,d5}
g2 = {d1,d3,d2}
g3 = {d4,d3,d5}

I have the following table called director_genre:

      director_id | genre       
       d1           g1
       d1           g2
       d2           g2
       d3           g1
       d3           g2
       d3           g3
       d4           g3
       d5           g1
       d5           g3

The output I want is

      genre |  director_id       
       g1      d1,d3,d5
       g2      d1,d3
       g3      d3,d5

The query I thought of is

SELECT genre
FROM director_genre
GROUP BY genre;

After this, I am not to put the logic as asked in the question.
Please help me to get this done.

I would suggest the following query:

SELECT d.genre, GROUP_CONCAT(director_id)
FROM director_genre d
WHERE EXISTS (SELECT *
              FROM director_genre d2
              WHERE d.director_id = d2.director_id AND d.genre <> d2.genre
)
GROUP BY d.genre;

The nested subquery will select only records of directors who are associated with at least 2 genres (for each record in d it looks whether there exists a record in d2 with the same director_id but different genre). Then they will be grouped by genre.

You want a list of (genre, director) where the director is also associated with another genre. Then group. This could be done like so:

select genre, group_concat(director_id separator ', ') as directors
from dg
where exists (
  select *
  from dg as x
  where x.director_id = dg.director_id
  and x.genre <> dg.genre
)
group by genre