It would be quite neat to be able to do that. Ancestry.com is another site that should offer something like that... enter your family tree and then pick some r

It would be quite neat to be able to do that. Ancestry.com is another site that should offer something like that... enter your family tree and then pick some random person who also has a family tree on file and show how you're related. They can't even do that within your own family tree (e.g. pick a person in your family tree and tell you "Augustus is your fourth cousin three times removed" or "Myrtle is your great-grandmother." It is an example of the traveling salesman problem but there are ways of optimizing that... think about chess, or how google maps and the other map programs give you a route to a destination. If they had to check every single intersection it would be NP-complete. Instead they use the distance between two points as a weighting factor and try to find major arteries near both points. I think you could do the same thing with Facebook et al - first look for common groups between people and then look for people who have pairs of common groups which would help to connect the people. But you would have to have a reasonably complete set of Facebook data to work on. I wonder if they'd mind if you crawled their entire network and then did it again every few days, just to keep things current?