connectedness and the decay of influence in social networks
I made passing reference in an earlier post to the idea of using decaying influence in a social network -- i.e., that the further someone is from me in my social network, the less influence they have on what I see. In eurekster, for example, single-hop friends would have far more effect on moving a possible link up in my search results than four-hop "friends". As I think about it, there's a more general question here: within some social network, how do you determine how connected two people X and Y are? This seems clearly an important general notion for social networks, with some tricky details to work out.
In friendster, your "network" is everyone within four hops of you. So essentially a person is fully connected (call it c(x,y)=1) if they are within four hops and unconnected (c(x,)=0) otherwise. Though in fact, friendster does make some distinctions -- if I recall correctly, you see only message board posts from your friends, and you can only send a friend request to someone who is within two hops. So you might come up with numbers like single-hop friends have a c() of 1, two-hop friends a c() of 0.75, and so on.
One distinction friendster does not make, however, is to measure how connected two people really are. For example, suppose X has two two-hop friends (i.e., friends of friends) Y and Z, but Y is a friend of many of X's friends and Z is a friend of just one. To friendster, these are essentially equivalent (though when X views Y's profile, he'll see the multiple links), but you can imagine trying to account for this in some connectedness metric.
In a conversation today, alice also reminded me that this should possibly take into account how close your friends are -- the friends of your best friend should have more weight with you than the friends of some acquaintance you met in a bar. I agree but am also leery of the whole ranking-your-friends concept. Though rough groups might help.
Does all this really matter? After all, it's not like you really do anything with your friendsters aside from figure out whether they're cute and browse their friendsters for more people to add to your network, right? Measuring connectedness may not seem so important right now while people are still just excited about just building these networks and talking within/about them. But as soon as we start to use them for other things (and I wouldn't be surprised to see them become more integrated into other kinds of software/websites -- social networking + product reviews and shopping, for example; eurekster is an example of integrating social networks into another function), people are going to want their closer friends and friends-of-friends to have more influence over what they see than some friend-of-a-friend-of-a-friend-of-a-friend yutz.
Here's what I'd like to see: a social networking system that is more integrated into other things I do regularly, like reading news/blogs and shopping for stuff. As I browse, I'm more likely to see things other people in my network like. But this influence is discounted the farther away people are. A simple discount per hop, somewhere between 0.5 and 1 (0.8 maybe; perhaps it should be customizable), and the math for how you weight someone to whom you have multiple links needs to be worked out (here's a hint, a two-hopper with lots of connections should have more influence than other two-hoppers but not as much as a one-hopper).