Logging into Facebook this morning I noticed a new feature called "People You May Known." The feature is exactly how it is described. The new People You May Known addition to Facebook analyzes similar friends of your friends. If Facebook finds a friend of a friend that is not already on your list of Facebook friends it suggest you might like to add them.
You'll spot the new People You May Know feature on your login page. Facebook showed me three profiles that I might know. When I clicked "see all" it took me to a larger page with more information, more profiles and more options.

(This is an expanded view of recommended friends.)
This Facebook User Gives the Feature a Thumbs Up
The most surprising part of this new add-on is that it works, and it works really well. Out of the 27 people it suggested that I may know, there was only one person that I didn't know, or at least didn't remember. The other 26 people I knew and some of which I began clicking on the convenient "Add To Friends" link. If you are still curious, it also lists what friends you both know to clarify any questions.
Given the complexity of making this work, you would have to assume it uses advanced algorithms to do the suggesting. I'll tip my hat to Facebook and the crew of developers. Good job putting something useful into your social networking platform.