Figure 1

Schematic representation of five simple models for faculty hiring. (a) Four large circles represent institutions, and filled circles represent faculty who graduated from the color-matched institutions. Grey links denote faculty hiring, including self-hiring. When a department j has an open position (a retirement), a new hiring event from institution i will occur with probability \(P_{ij}\), determined by a hiring model. All institutions are assigned a prestige rank, where a high rank \(r_{i}\) denotes high prestige, calculated via SpringRank [6]. (b) Mathematical definition of \(P_{ij}\) for five hiring models, showing how each model formalizes a different notion of institutional prestige: the number of faculty produced by an institution i (\(k_{i}\)), the number of previous hires from i at j (\(k_{i\rightarrow j}\)), the rank of i (\(r_{i}\)), the weighted number of faculty produced by i (\(k_{i}w_{i}\)), and the weighted number of previous hires from i at j (\(k_{i \rightarrow j}w_{i}\)) with a preference strength β of an institution’s prestige