A model of collaboration network formation with heterogeneous skills

Collaboration networks provide a method for examining the highly heterogeneous structure of collaborative communities. However, we still have limited theoretical understanding of how individual heterogeneity relates to network heterogeneity. The model presented here provides a framework linking an individual’s skill set to her position in the collaboration network, and the distribution of skills in the population to the structure of the collaboration network as a whole. This model suggests that there is a non-trivial relationship between skills and network position: individuals with a useful combination of skills will have a disproportionate number of links in the network. Indeed, in some cases, an individual’s degree is non-monotonic in the number of skills she has—an individual with very few skills may outperform an individual with many. Special cases of the model suggest that the degree distribution of the network will be skewed, even when the distribution of skills is uniform in the population. The degree distribution becomes more skewed as problems become more difficult, leading to a community dominated by a few high-degree superstars. This has striking implications for labor market outcomes in industries where production is largely the result of collaborative effort. Acknowledgement. Thanks to Scott Page, Ross O’Connell, Lada Adamic, and Robert Willis for their valuable input. This work was completed with the help of funding from the NSF and computing resources from the University of Michigan Center for the Study of Complex Systems. 1 ar X iv :1 11 2. 51 21 v2 [ ph ys ic s. so cph ] 2 6 Ju l 2 01 6