Brian Uzzi, Roger Guimera, Jarrett Spiro, Luis Amaral
This paper could almost be considered the culmination of everything I've read on my list. It has a lot of elements, network analysis, network modeling, empirical data, and empirical verification of a model. And it's all wrapped up by a veneer of Broadway musicals. I'm a fan of Brian Uzzi and Roger Guimera, they both do some very interesting work. In this case, they and their coauthors hope to explain the mechanisms of growth for bipartite networks. They examine empirical data of the growth of co-workers on broadway musical playbills and suggest a model where the type of link is important. They even analytically solve the model and make predictions which they successfully test on their data.
When researchers construct networks from existing data we have to ask questions such as how they define actors and how they define links. In this case the network is originally bipartite. The actors are directors, costume designers, actors (the acting kind) who appear on a playbill for a musical. They form links by being on the same playbill together. The network when it is expressed and modeled is not bipartite though. Bipartite networks are two-colorable, meaning you can assign every node one of two colors and no adjacent nodes will have the same color. A true representation of the network would have actors and playbills as two kinds of nodes in the network. Instead they treat the playbill as creating 'cliques' where every node in the playbill is connected to every other node in the playbill. As the network evolves there aren't so much as links being created so much as cliques.
When the network starts out there are only newcomers. Newcomers have collaborated on their first work and appear on a playbill for the first time. Eventually we see incumbents who have worked before and they can form links with other incumbents. There are several levels of links N-N (newcomer, newcomer), N-I (newcomer, incumbent), I-I (incumbent, incumbent, but the actors have not collaborated before, they're just incumbent), and I-R (same as incumbent incumbent except that both actors had collaborated on something before. These types of links, it is hypothesized, drive the emergence of the fully connected network.
There are a number of parameters: p, the probability of linking to an incumbent; q, the probability of linking to a past collaborator; m, the "team-size" which means the number of people on the playbill; and f, the amount of time you keep an inactive actor on the field before removing him.
The model displays some interesting dynamics. The image above is from a NetLogo simulation of the model you can play with. I liked setting all the variables constant but varying, up and down, the q variable. This made the network very modular, while otherwise it would have just been a single densely connected community.
The best part, which is something terribly lacking from most models, is the empirical validation. They analytically solve for the predicted fraction of of N-N, N-I, and I-I and find that all the parameters but p drop out (which is interesting). Then they show that the curves match the empirical data very well.
I'm left wondering what else could be done with this model. If it is a valid model then what sort of perturbations can we make that produce interesting predictions that we can go out and test for? Like varying the probability of working with a past collaborator, does that really produce more modular networks, like I was finding? Are there social systems where that value actually does oscillate where we can test the modularity? Conference papers can be pretty cool sometimes.
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