The final talk at the networks conference was from Albert-László Barabási of Northeastern University. I was sitting with Jen Victor during the talk, and while we loved it, it made realize just how poor a grasp most of us in political science have of the network tools we're playing with.
If I can convey Barabási's points correctly, there are huge differences between random networks (which would exist if every individual just randomly connected to others) and the way most networks actually occur in nature. In random networks, just about all actors would have about the same number of connections as everybody else. An example would be the U.S. highway system. Most major cities have two or three highways going through them; very few have just one or more than four. This is a very democratic, egalitarian network.
It's also a very rare network. What we more often see are what are called scale-free networks, in which a few hubs are highly connected and everyone else just has one or two connections. The airline system looks like this, with a few major cities providing the connections for hundreds of other cities. Take out a bunch of minor actors, and the network stays intact. Take out a few hubs, and the network collapses. We tend to see scale-free networks all over the place, from the structure of cells to the links of the Internet.
This kind of terminology and framework seems really important, and I didn't have a great concept of this stuff until today's talk. In fact, I don't think I really understood the distribution of the data I've been working with. That's bad! Jen and I were perturbed that we're kind of working in the dark on this stuff, and we're allegedly leading scholars in this area. What's more, there are mathematicians who do understand this stuff who are no doubt laughing at us right now like we're chimps trying to operate a Blackberry.
I suppose this happens any time a social science imports a method from another field, but it's nonetheless disturbing.