First a great post on apophenia about the problems with "friend" connections in social networks and the definition of fan. I agree, anyone can be a fan and perhaps even a silent fan.
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?
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?
Regarding Danah’s post I wish she mentioned the rival problem in social networks. How do you measure your relation to a rival? Certainly not by inviting them to be a friend, rather you probably function as a stalker (flickr would have this data, repeat views of a non-friend when sets have a high duplication percent…)
Second is a rehash of some interesting graphing tools: