Facebook – Result starts with someone who is not a friend in Facebook search

Facebook has access to all friendship-data on their site, even if you lock down the privacy settings. As an addition many users share their contact-book or even e-mails with Facebook. Most peoples have filled out their profile quite decent so it has data about your school, your employer, your current place, your interests and so on. Although Facebook states it does not use it, they can track all users (and even non-users) across many websites via the "like"-button which is transcluded directly from Facebook.

From this data it can calculate this friend requests.

I don't know for certain (I don't work for Facebook!), but from my experience it seems to bring back results in (approximately) the following order:

1. From your friends
2. From your friends friends
3. People with common interests (liked pages, shared groups etc.)

After this it starts to become more guesswork, but I suspect that home town, shared work places etc all come into play as well.

With more than 500 million users there's a lot of data and existing connections they can use to base their heuristics on