How to produce a better circle-map visualization
Below are two of my initial drafts (produced by matplotlib library in python). They visualize 12,000 unique votes on 700 status updates in a social network.
The first one shows nodes on a circle and connects each note to its neighbor with a straight line. The other one connects nodes with a Bézier curve with four control points (starting node, end node, a point that is 2/3 of the way between the start point and the center, a point that is 2/3 of the way between the center and the end point). I still do not know what is the best way to draw arcs for a circle map and perhaps a circular arc might work better than a Bézier curve. but I’ve been happy with the Bézier curve so far. (make sure you take a look at the animations too ,  they are large files so please wait a little for the animated gif to load completely)