I came across this thing a few days ago. I normally would not pay attention, but it was the "math" part that totally amused me. For some reason, a lot of people use circles when talking about social influence on the web. Circles are simple, easy to understand, and um, totally wrong.
There's a plain reason for it: the image above make us think that interpersonal influence is no different from mass media influence. We "broadcast" to our "followers". The fun part? Graphs like this are used by social media experts, who like to sometimes claim that mass media are dead. And then they go and draw concentric circles to describe the "new" influence of social media.
Aside of the fact that this kind of thinking is oversimplified and wrong for the obvious reason (a person who's a flickr follower is also a twitter follower is also a facebook friend, so these circles are hardly ever concentric), there is a more important one. Interpersonal influence is not broadcast. Simply put: how influential you are going to be does not only depend on you, it depends on how influential your friends are. That is, your influence is the outcome of their network even more so than yours. That applies to plain scale (how many people are in their network), but also on scope (who they are). So, hard as it may be on the ego, you are not at the center.
A real world example: I have started this blog in September 2008, less than 6 months ago. It was pretty much silence all around until Brian linked to a post he liked in his Twitter update (Brian currently has near to 5,000 followers on Twitter, at that point a mere 3,000). The traffic spiked. Then, there was a little but nevertheless totally endearing spat with Josh Spear here, which created traffic, too. And then, some time later Noah liked something on my blog, linked to it on his blog and on the Barbarian Group's blog and the traffic spiked again. More people started coming. Then Michael accidentally discovered my blog in his Google alert (this is why it helps linking to other people), really liked it, and started regularly linking back to it. At this point, I started having a steady stream of traffic. None of it because of my own (rather limited) networks of influence (FB = 204 friends; Twitter = 57 followers (someone left today); Flickr = don't have an account). It is because of the size of their networks and the influence they already have (which they probably earned in the similar fashion at some time in the past). Simply said, my influence is the function of their networks.
If it were up to my poor network only, I would have to rely on the randomness of Google (not that anything is wrong w google -- it's the best serendipity machine ever & the largest possible network). But the best thing ever is the web is kinda random network (with a group structure ;). No more circles, please.