So the nice thing about pajek, and some other network displaying software, is that you can use algorithms that will attempt display things that are closely related to each other closer together. If I were going to produce your graphic I would:

1. Get the graph in memory some how, for one this size I would just set up some hash maps in irb
2. Write a text file where each line consists of two nodes that are connected seperated by a tab.
3. Use the software here: http://vlado.fmf.uni-lj.si/pub/networks/pajek/howto/text2pajek.htm to get a pajek file
4. Open it in pajek and preform a physics based layout algorithim
5. Export to png

It's pretty cool what you can get out form this (I made this: http://a3.twimg.com/profile_images/56256047/bhtv3d.png Network of bhtv coversations) and there's a lot to be gained by checked out what ends up near the center etc.

Let me know if you have any questions. I'd be glad to help.