Exponential random graph modeling of a faculty hiring network: The IEOR case

Faculty hiring networks consist of academic departments in a particular field (vertices) and directed edges from the departments that award Ph.D. degrees to students to the institutions that hires them as faculty. Study of these networks has been used in the past to find a hierarchy, or ranking, among departments, but they can also help reveal sociological aspects of a profession that have consequences in the dissemination of educational innovations and knowledge. In this article, we propose to use a new latent variable Exponential Random Graph Model (ERGM) to study faculty hiring networks. The model uses hierarchy information only as an input to the ERGM, where the hierarchy is obtained by modification of the Minimum Violation Ranking (MVR) method recently suggested in the literature. In contrast to single indices of ranking that can only capture partial features of a complex network, we demonstrate how our latent variable ERGM model provides a clustering of departments that does not necessarily align with the hierarchy as given by the MVR rankings, permits to simplify the network for ease of interpretation, and allows us to reproduce its main characteristics including its otherwise difficult to model presence of directed self-edges, common in faculty hiring networks. Throughout the paper, we illustrate our methods with application to the Industrial/Systems/Operations Research (IEOR) faculty hiring network, not studied before. The IEOR network is contrasted with those previously studied for other related disciplines, such as Computer Science and Business.