Circos is a project by Martin Krzywinski that lets you upload genomic data and visualize it as a network like the one above.
It is easy to plot, format and layer your data with Circos. A large variety of plot and feature parameters are customizable, helping you make the image that best communicates your data. You supply your data to Circos as flat files (e.g. GFF format), tell Circos what you want plotted using the configuration file, and then create the image.
While Circos is developed in the interest of visualizing genomic data, it is general enough that you can use it with other types of data that show relationships. The New York Times debate graphic is the first thing that comes to mind. Anyone want to give Circos a spin? Post a link to your image in the comments.