If the people who talk the most gravitate to the center, and each angular position is given by last time they are seen (and then converted to degrees), the above (clickable) plot results.
Regarding time, this plot shows 1440 minutes in 360 degrees. Midnight is to the East (0 degrees) and Noon is to the West (180 degrees). Also the log used for this plot is only for two relatively quiet days. More would make for a cluttered graph!
Animation would be interesting – showing points jiggle into place. Because this is time-based, showing a radar sweep might be helpful to minimize clutter.
For the simple Perl code that produces this visualization, check out vizirc on github.
And by the way, “who talks” is just a metaphor here. The data could be anything measured in time with magnitude. The connections between points can be any computed relationship.