What type of database can I use to store mutual scores between every combination of users? Let's say I have an application that calculates and stores a mutual score between every combination of users. 

I'm currently using Postgres to store this information. 

So if my system had users with id 1, 2, and 3 that table might look like

CREATE TABLE scores (id,user_id,friend_id,score)
AS ( VALUES
    ( 1, 1, 2, 15.2 ),
    ( 2, 2, 1, 15.2 ),
    ( 3, 1, 3, 19.7 ),
    ( 4, 3, 1, 19.7 ),
    ( 5, 2, 3, 21.0 ),
    ( 6, 3, 2, 21.0 )
);


As you can see, the data itself is pretty simple. 


Every combination of users has a mutual score calculated between them (the derivation of that score or what it means isn't important here) and I store it in the table. 
Because I could look up either user, I have to store the pairings "both ways" (e.g. 1 -> 2 and 2 -> 1)


The problem is that this increases quadratically. With 10,000 users there are 100 million records in this table. With 100,000 users (which is a reasonable scope for my app) there would be 10 billion records. 

So my question is - surely Postgres can't be the most scale-able way to store this information right? I don't need access to it constantly, just periodically when I'm running a batch job so I'm happy to store it in some separate type of DB on a separate server. 

What kind of DB specializes in storing this type of paired data and can perform quick reads? 

For example, I commonly query for all the ranked friends of a given user with SELECT friend_id FROM my_table where user_id = ? ORDER BY score DESC so I'd like to run the equivalent of that query on this new database. 

Thanks!

P.S Someone had suggested a Graph DB - didn't know if that would apply here.
Because I could look up either user, I have to store the pairings "both ways" 


Well, that's not true. You could normalize the data because the relations aren't directed anyway.

CREATE TABLE scores (
  user_id   int,
  friend_id int,
  score     int,
  CHECK ( user_id &lt; friend_id ),
  PRIMARY KEY (user_id, friend_id)
);

INSERT INTO scores (user_id, friend_id,score)
VALUES
  ( 1, 2, 15.2 ),
  ( 1, 3, 19.7 ),
  ( 2, 3, 21.0 );


Now you can find the relation easy.

SELECT *
FROM scores
WHERE user_id = 1
  AND friend_id = 2;


If you don't want to put the rule in the app, just rewrite the query into.

SELECT *
FROM scores
WHERE (user_id, friend_id) =
  ROW( least(1,2), greatest(1,2) );