Global and local preferential attachment in faculty hiring

Patterns of faculty hiring in academia can be represented as a network, with directed, weighted edges representing the number of Ph.D. graduates that are produced by one institution and hired by another. The structure of these networks is dominated by two distinct heavy-tailed distributions: (i) of faculty reach (out-degree) and (ii) of faculty flow (edge weight). To explain the emergence of these patterns, here we introduce a minimal model that combines global preferential attachment (in which high faculty reach leads to increased reach) and local preferential attachment (in which high faculty flow leads to increased flow). With only two parameters, reflecting the strengths of global and local preferential attachment, our model is able to quantitatively predict the distributions of out-degree and edge weight observed in faculty hiring. These results demonstrate that two distinct rich-get-richer mechanisms are needed to understand the heavy tails of faculty hiring, offering insights into the emergence of hierarchy, prestige, and systematic inequalities.