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 gm-index. It has some important differences from the mentorship h-index or the hm-index. We compute the values of the hm and gm 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 hm-index. Moreover, the g m-index decays less rapidly to zero than the hm-index. It appears the g m-index can be used to discriminate between researchers with the same hm-index. We study how these mentorship indices are correlated with other indicators of academic success, and how they are correlated across generations of researchers.