I just learned that Wolfram Alpha, the "computational knowledge engine," can do an analysis of your Facebook account data. Run a "facebook report" in the main box, and it will get you started.
It needs permission to see into Facebook and you need to set up a Wolfram Alpha account (free). It gives you basic information, along fun statistics: when you usually post - and when you post updates vs. photos; demographics of your friends (gender, age, relationship status, location, language); and the social graph. Each of these has more detail - I took a peak at the Zodiac sign distribution, and I was surprised to see a lumpy distribution (highest peak with Virgo).
This network (or this image online) is what my network looks like in their visualization with some notes on the general groupings. As usual with any network analysis, there are some groups that are fairly self-contained, and others that are highly interconnected. My Boston network is a good example of that, beyond neighborhood-related friends, all the people I know in Boston are heavily connected across many networks in Boston and beyond.