Network-based indices of individual and collective advising impacts in mathematics

Advising and mentoring Ph.D. students is an increasingly important aspect of the academic profession. We define and interpret a family of metrics (collectively referred to as “a-indices”) that can potentially be applied to “ranking academic advisors” using the academic genealogical records of scientists, with the emphasis on taking into account not only the number of students advised by an individual, but also subsequent academic advising records of those students. We also define and calculate the extensions of the proposed indices that account for student co-advising (referred to as “adjusted a-indices”). In addition, we extend some of the proposed metrics to ranking universities and countries with respect to their “collective” advising impacts, as well as track the evolution of these metrics over the past several decades. To illustrate the proposed metrics, we consider the social network of over 200,000 mathematicians (as of July 2018) constructed using the Mathematics Genealogy Project data.