Well, I think the easiest way to understand this is to see it in action!

1/Go to this page:
http://apps.asterisq.com/mentionmap/#hashtag-sharepoint

2/ Watch the graph build itself and start interacting with it
and/or
3/ Enter your Twitter id in the green text box, on the top left

How it works (source Asterisq): Mentionmap loads each user’s Twitter status updates (tweets) and finds the people and hashtags they talked about the most.[…] In this data visualization, mentions become connections.

Now, here is the reason why Mentionmap immediately caught my attention: the idea is not new to me, this network graph is something I already thought about in the past. I never blogged about it, but back in January I was in contact with Daniel McLaren, the author of the application, and built a proof of concept, based not on Twitter but on Technorati:
http://www.pathtosharepoint.com/Pages/constellation_roamer.html
Click for example on endusersharepoint.com to see which blogs linked to it (remember, the data is from January).

I dropped the idea because it didn’t work out so well with Technorati – the data was too scarce to be meaningful.

So, let me know if Mentionmap works for you! Does the graph help you discover useful connections?

And for Lord of the Rings fans: check out this experiment on timeline visualization, also by Daniel McLaren.