Relational databse design to represent similarity between rows of same table - postgresql

Question

For background purposes: I'm using PostgreSQL with SQLAlchemy (Python).
Given a table of unique references as such:
references_table
-----------------------
id | reference_code
-----------------------
1 | CODEABCD1
2 | CODEABCD2
3 | CODEWXYZ9
4 | CODEPOIU0
...
In a typical scenario, I would have a separate items table:
items_table
-----------------------
id | item_descr
-----------------------
1 | `Some item A`
2 | `Some item B`
3 | `Some item C`
4 | `Some item D`
...
In such typical scenario, the many-to-many relationship between references and items is set in a junction table:
references_to_items
-----------------------
ref_id (FK) | item_id (FK)
-----------------------
1 | 4
2 | 1
3 | 2
4 | 1
...
In that scenario, it is easy to model and obtain all references that are associated to the same item, for instance item 1 has references 2 and 4 as per table above.
However, in my scenario, there is no items_table. But I would still want to model the fact that some references refer to the same (non-represented) item.
I see a possibility to model that via a many-to-many junction table as such (associating FKs of the references table):
reference_similarities
-----------------------
ref_id (FK) | ref_id_similar (FK)
-----------------------
2 | 4
2 | 8
2 | 9
...
Where references with ID 2, 4, 8 and 9 would be considered 'similar' for the purposes of my data model.
However, the inconvenience here is that such model requires to choose one reference (above id=2) as a 'pivot', to which multiple others can be declared 'similar' in the reference_similarities table. Ref 2 is similar to 4 and ref 2 is similar to 8 ==> thus 4 is similar to 8.
So the question is: is there a better design that doesn't involve having a 'pivot' FK as above?
Ideally, I would store the 'similarity' as an Array of FKs as such:
reference_similarities
------------------------
id | ref_ids (Array of FKs)
------------------------
1 | [2, 4, 8, 9]
2 | [1, 3, 5]
..but I understand from https://dba.stackexchange.com/questions/60132/foreign-key-constraint-on-array-member that it is currently not possible to have foreign keys in PostgreSQL arrays. So I'm trying to figure out a better design for this model.

Answer 1

I can understand that you want to group items in a set, and able to query the set from any of item in it.
You can use a hash function to hash a set, then use the hash as pivot value.
For example you have a set of values (2,4,8,9), it will be hashed like this:
hash = ((((31*1 + 2)*31 + 4)*31 + 8)*31 + 9
you can refer to Arrays.hashCode in Java to know how to hash a list of values.
int result = 1;
for (Object element : a)
result = 31 * result + (element == null ? 0 : element.hashCode());
Table reference_similarities:
reference_similarities
-----------------------
ref_id (FK) | hash_value
-----------------------
2 | hash(2, 4, 8, 9) = 987204
4 | 987204
8 | 987204
9 | 987204
To query the set, you can first query hash_value from ref_id first, then, get all ref_id from hash_value.
The draw back of this solution is every time you add a new value to a set, you have to rehash the set.
Another solution is you can just write a function in Python to produce a unique hash_value when creating a new set.