Thanks to
nwhyte for pointing me at
Gephi, which is a very spiffy graphing tool. You can use it to make a big map of your FB friends, and how they all connect.
There's a fantastic guide to how to use it
here, which I carefully followed my way through, tweaking numbers until I found something that worked well. And I ended up with this:

That's the absolutely tiny 65k version. The version where you can make out people's names is
here, because it's 2.5MB and I didn't want to kill your internet by embedding something that large.
Apologies to a few of you for where you ended up - it's a semi-automated process, and while I'm sure (for instance) that
rosamicula will be grumpy at being lumped in with the SF fans in this case I'm afraid you are you who you know :->