This post on Social Flow's website does a great job of creating a visual representation of the network that drove the Stop Kony message into a viral tizzie over the course of the last week. Moreover the article does a great job of pinpointing the underlying mechanisims and prerequisites that enabled the video to take off and go viral so quickly.
First Invisible Children had a pre exiting network to seed and spread the video.
Secont they had a preexiwting network of Celebrities associated with their cause.
Third they activated their network all at once, and drive them to not only share their own message but also pressure the celebrity base.
The net effect is a verry fast and furrious publicity spike that creates ripples and aftershock spikes over the course of a week. Like a pebble landin in a pond or an earthquake there is an initial surge of traffic and then subsequent smaller rushes of eneregy. The real question posed is if this is a sustainable model for garnering attention or not.