gm-index: a new mentorship index for researchers.

Advisor–advisee relationships in academic genealogy offer opportunities to understand the contribution of a mentor in shaping the research community. In this paper, we adapt the bibliometric g-index to study the mentorship role of a researcher. We call the new index g m -index. It has some important differences from the mentorship h-index or the h m -index. We compute the values of the h m and g m indices for researchers indexed in the Mathematics Genealogy Project and the Academic Family Tree. We observe for the majority of researchers, these index values are zero, but in non-zero cases, sometimes, the g m -index can be significantly higher than the h m -index. Moreover, the g m -index decays less rapidly to zero than the h m -index. It appears the g m -index can be used to discriminate between researchers with the same h m -index. We study how these mentorship indices are correlated with other indicators of academic success, and how they are correlated across generations of researchers. [ABSTRACT FROM AUTHOR]