(originally posted on centrality)

Network analysts often speak about (un)directed graphs. In essence, this refers to whether or not someone you know knows you. If reciprocity is required by the system, it’s an undirected graph. The vast majority of online social networking tools assume that users are modeling friendship and thus if you’re friends with someone, they better damn well be friends with you. As such, they use undirected graphs and you are required to confirm that they are indeed your friend.

Well, what about fandom? Orkut actually put the concept of fan into their system, but in order to be someone’s fan, you had to be their friend first. Baroo? I’ve noticed that Friendster introduced fans, although it is not consistent across the site; the system decides who is celebrity. I can be a fan of Pamela Anderson but i cannot be a fan of Michel Foucault or Henry Jenkins. While i can understand that the former is clearly a Fakester, the latter is actually a real academic with a Friendster Profile that i genuinely admire (far more than Ms. Anderson). Even on MySpace where bands have a separate section, i have to add them to my friends; i cannot simply be fans.

The world is not an undirected graph and very little about social life online is actually undirected. Many social relations are unequal; they are rooted in directional graphs – fandom, power, hierarchy. So why do we use undirected models?

Of course, there are many systems that have directed graphs. I can read blogs by bloggers who who don’t read me; blogrolls are directed. I can have friends on LiveJournal that do not reciprocate. I can subscribe to del.icio.us feeds of people that i admire without forcing them to do the same. I can make a Flickr user a contact simply so that i can watch their photos. I do all this because i know the world is not undirected.

Part of the problem is that we’ve built a model off of social networks instead of attention networks and there’s a very subtle difference between the two. Attention networks recognize power. They recognize that someone may actually have a good collection of references or be a good photographer and that someone else may want to pay attention to them even if their own collections are not worthy of reciprocation. Attention networks realize that the world is not an undirected graph.

There are many good reasons to use attention networks in systems instead of social networks. Do you really want to force people to get permission to subscribe to public material of someone else? Do you really want to put people through the awkwardness of having to approve someone that they don’t know simply because one person respects the other? Of course, the awkwardness of social networks does not disappear simply by having directed graphs. Reciprocity is still an issue whenever the networks are performative (visible as a statement of connection). This is most apparent in the blogging community where people feel insulted that they are not included on the blogroll of a blog that they read regularly. Thus, people feel the need to perform a relation of someone that they do not read simply for good social measure.

Attention networks are far more visible when people actually use the network for some purpose. Friendster networks are meant to be performative first and foremost. There’s minimal cost to having more friends. It may foul up your gallery searches but, really, does it make a difference if you see 4,325,935 people instead of 4,311,266? Attention networks like LiveJournal and Flickr combine the network with the subscription process. You want to keep your Friends page clean and to only get information from people you care about. Of course, LJ also recognizes that there are times when you need plausible deniability. It allows you to create a separate group of LJ folks that you actually watch (separate from your “friends” list). The subscription process is inherently a process of attention relations, not friendship.

Of course, the computation needed for directed graphs is much greater than for undirected graphs. Is that the main reason that most services require reciprocity? Even when it’s not the best mechanism for the system? Or are there other reasons why folks are obsessed with undirected graphs?