Mathematical relations of the h-index with other impact measures in a Lotkaian framework

Abstract

In a Lotkaian framework there exist formulae for impact measures such as the h-index, g-index, R-index and Randić’s H-index. Given two situations in which the h-indices are equal, we establish the functional relation of the R-, g- and H-index of Randić with the total number of papers. In all cases we have adecreasing relationship which can also be explained from a concentration point of view. Variants of relations between these measures are also proved. We also prove a Lotkaian formula for the π-index of Vinkler. We indicate that the square root of this index is better in line with the other indices and we also show that the previously established results on the h-, g-, R- and H-index are not valid for the π- or -index.