A few months back, I had been analyzing Twitter's social network. This meme was recently picked up for a photo essay in March/April issue of the Technology Review Magazine. You can read an online version here. It also has a number of really cool visualizations from other researchers who have been studying the "social graph". For this visualization, I had used the Large Graph Layout (LGL) tool to visualize the social network on Twitter. Following is a graph constructed using contacts from about 25K users.
One of the challenges in laying out large graphs and social networks is that it is often hard to interpret what these graphs signify. To get a better understanding of the information in such networks, we inevitably need to look into the underlying community structures. My paper titled "Why We Twitter: Understanding Microblogging Usage and Communities" tried to answer these questions.