Most of us have a list of friends at that numbers in the hundreds or even thousands, but I’m sure that most of us only consider some proper subset of them friends. Whether the complement of that set is the remnant of people who randomly friended you before coming to Cornell or just people you don’t talk to so often, the fact is that not all of our friendships have quite the same meaning.

Of course, we know that we can’t label our ties with a W or a S, like we did in approximating the strength of links in certain sorts of social networks early in the term. This sort of rudimentary labeling was surely useful in formalizing the intuition of the difference between a friend and an acquaintance for the purposes of an introductory class about networks. However, I think it would be pretty uncontroversial to assert that the Facebook’s lack of explicit edge-labeling is a very good thing. Surely it would be a nightmare to try to group our friendships into categories. It would probably introduce all sorts of other conflicts as well–I’d probably be at least slightly bothered in cases where the person with whom I shared an edge disagreed about the character of that tie.

With that said, logging into The Facebook today, I noticed a new feature: based on your existing friendships, the service will enumerate people (who aren’t yet your friends) who are likely to be your friends. I laughed when I saw it, because I think this is clearly a no brainer that should have been done at least two years ago. Check out a screen shot:

Surely, this feature is intended to capture the same sort of intuition as we did in our discussion of triadic closure that we discussed earlier in the course: if a person x shares a friendship with a person y and a person z, then it is likely that y and z are friends. Of course, this generalizes it somewhat in some ways that might be unknown to us and are likely very interesting.

But beyond that, I think there is an even more interesting observation to be made by thinking about the application’s suggestion to use the feature so that the results can become better for you. Clearly the clever engineers at the Facebook have some cute algorithmic tricks up their sleeves here. If it is indeed possible to improve your results by offering feedback, then perhaps the application is capable of learning which sorts of ties are stronger than others.

Suppose that you are friends, on the Facebook, with A, B, C, and D. Suppose also that you are friends (but not on the Facebook) with E as well. Suppose A and B are Facebook friends with E, and suppose that C and D are Facebook friends with F, who you might know but wouldn’t consider a friend. Now, suppose that the Facebook suggests that you might be friends with E based on your friendship with A and B and that you might be friends with F based on your friendship with C and D. Naturally, you might add E as a friend based on this suggestion, but not F. This gives reason to believe, perhaps, that A and B are closer friends to you than C and D are.

So imagine that it does really turn out to be the case that the Facebook can gather enough data from this feature such that it can apply fancy algorithms to try to approximate the strength of ties. Yeah, there are a lot of ifs buried in there. But seriously: sweet.