Ari Sternberg of Facebook submits this cool query based on the newly released FQL:

Oh yeah, also, I'm curious if you guys come up with any cool FQL queries. Here's one that you might find interesting:

SELECT uid1, uid2
FROM friend
WHERE uid1 IN (SELECT uid1 FROM friend WHERE uid2=UID)
AND uid2 IN (SELECT uid1 FROM friend WHERE uid2=UID)
AND uid1 < uid2

Replace UID with the logged in user's id (e.g. 211031 for me).

This gets your whole friends map in (for me) about 5 seconds. As opposed to the many minutes that most of those friend visualization apps take using the old API and friends.areFriends.

Oh and btw, while I encourage you to try out absurd queries in the test console, please be reasonable and don't do these things in a tight loop in your program or anything. That is, you can do a big query, but don't do *too* often, or at least warn us first or something

I tried it in the test console and it works great.