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.

中文翻译：

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基于网络的个人和集体对数学的影响的指数

为博士生提供指导和指导 学生是学术界越来越重要的方面。我们定义和解释了一系列指标（统称为“ a-指标”），这些指标可以利用科学家的学术谱系记录潜在地应用于“对学术顾问进行排名”，重点不仅要考虑由学生提供个人建议，但随后还会提供有关这些学生的学术建议记录。我们还定义并计算了建议的指数的扩展范围，这些扩展范围考虑了学生的共同建议（称为“调整后的A指数”）。此外，我们将一些拟议的指标扩展至大学和国家/地区，以就其“集体”建议的影响进行排名，并跟踪这些指标在过去几十年中的发展。