LinkedIn appears to build "social graphs" based on profile views. If person A visits the profile of person B and C it is quite likely that some form of relationship exists (perhaps an inverse relationship too). It doesn't just have to be profile views -- LinkedIn most likely keeps track of search terms too. If a random unknown visitor comes along and searches for both "Person A" and "Person C" then it is likely that a connection exists between these two persons.
It would be easy to train this system by displaying a "guess" (a friendship recommendation for person A) to persons B and C. If person B or C show interest in the recommendation then perhaps a relationship exists. Guesses could also be formed by comparing keywords/metadata found on profiles in two different social circles.
The reason I mentioned LinkedIn is that I think they do a better job of recommending/guessing who your acquaintances are than Facebook.
I was about to post about LinkedIn too. I am convinced it uses, among others, reverse view lookups. I have had suggestions for people I know whose LinkedIn profile I had never viewed or searched for myself; the only explanation is they had looked for me. I don't know if it's because I interact with it more frequently and using real personal info but its "people you may know" predictions are eerily more accurate than FB, or anything else for that matter.
It would be easy to train this system by displaying a "guess" (a friendship recommendation for person A) to persons B and C. If person B or C show interest in the recommendation then perhaps a relationship exists. Guesses could also be formed by comparing keywords/metadata found on profiles in two different social circles.
The reason I mentioned LinkedIn is that I think they do a better job of recommending/guessing who your acquaintances are than Facebook.