WolframAlpha has a tool that will analyze your Facebook network. I saw this awhile ago, but HollyLynne reminded me of this recently, and I tried it out. You need to give the app(?) permission to access your account (which I am sure means access to your data for Wolfram), after which you are given all sorts of interesting, pretty info. Note, you can also opt to have Wolfram track your data in order to determine how your network is changing.
Some of them are kind of informative, but others are not. Consider this scatterplot(???)-type plot that was entitled “Weekly Distribution”. Tufte could include this in his next book of worthless graphs.
There are other analyses that are more useful. For example, I learned that my post announcing the Citizen Statistician blog was the most liked post I have, while the post showing photographic evidence that I held a baby as far back as 1976 was the most commented.
This plot was also interesting…too bad it is a pie chart (sigh).
There is also a ton of other information, such as which friend has the most friends (Jayne at 1819), your youngest and oldest friends based on the reported birthdays, photos that are tagged the most, word clouds of your posts, etc.
This network was my favorite of them all. It shows the social insiders and outsiders in my network of friends, and identifies social connectors, neighbors, and gateways.
Once again, kind of a cool tool that works with the existing data, but there does not seem to be a way to obtain the data in a workable format.