Genealogical index: A metric to analyze advisor-advisee relationships

Academic genealogy can be defined as the study of intellectual heritage that is undertaken through the relationship between a professor (advisor/mentor) and student (advisee) and on the basis of these ties, it establishes a social framework that is generally represented by an academic genealogy graph. Obtaining relevant knowledge of academic genealogy graphs makes it possible to analyse the academic training of scientific communities, and discover ancestors or forbears who had special skills and talents. The use of metrics for characterizing this kind of graph is an active form of knowledge extraction. In this paper, we set out a formal definition of a metric called 'genealogical index', which can be used to assess how far researchers have affected advisor-advisee relationships. This metric is based on the bibliometrics h-index and its definition can be broadened to measure the effect of researchers on several generations of scientists. A case study is employed that includes an academic genealogy graph consisting of more than 190,000 Ph.D.s registered in the Mathematics Genealogy Project. Additionally, we compare the genealogical indices obtained from both the Fields Medal and Wolf Prize winners, and found that the latter has had a greater impact than the former.