As far as I'm aware it comes down to interactions. It'll be the people that you publicly interact with the most via wallposts, comments and likes. It's probably not completely controllable by just you, it'll work both ways.

My best guess is a point system, for every like, comment and wall post there will be x points for that interaction. The points you and any friend you have would then be totalled up to give a point score to the friendship.

So the calculation is probably something like: [Your interactions] + [Friends interactions] = Strength of friendship.

So the strongest fb friendships you have probably sit on your profile, it looks like there's no order to the friends that appear there though and occasionally a couple will change upon refreshes. Facebook probably builds a list slightly larger than the number of slots available and randomises the positioning.

/quick guess