Asymmetric links in random networks and the diameter of the “Blogosphere”

Yesterday’s post had some discussion about complex, scale-free network theory. Since I posted that, I’ve been wondering about network theory as it relates to the blogging community. By now, everyone has seen a “blogroll” list which is essentially a listing of the ideological connectivity of that particular blog (or “node” in the language of network theory). The odd thing about blogrolls is that they are asymmetric links. I may have In the Pipeline in my blogroll, but Derek doesn’t link back to me (at least not yet). So the link between the “OpenScience” and “In the Pipeline” nodes is asymmetric. What I don’t know yet is whether this kind of network has different kind of fragility or robustness under random node removal than networks with symmetric links.

I’ll have to ask László about the robustness or fragility of networks with asymmetric links. Surely someone has worked on this problem, because flow directionality is a pretty important property of highways, railroads, and airlines.

We do know that the “blogosphere” (I hate that word) is probably a scale-free network. There are some blogs (nodes) which are linked by very few others and some which are linked by a nearly infinite number of other blogs (Instapundit and DailyKos come to mind). So the distribution of the number of blogs with a given number of links to it is almost certainly a power-law distribution. For a better description, there a good wikipedia entry on Scale-free networks.