Egghe, L. 2011. Mathematical relations of the h-index with other impact measures in a Lotkaian framework. MATHEMATICAL AND COMPUTER MODELLING 53 (5-6): 610-616

[Eugene Garfield]

Egghe, L. 2011. Mathematical relations of the h-index with other impact 
measures in a Lotkaian framework. MATHEMATICAL AND COMPUTER MODELLING 
53 (5-6): 610-616.

Author Full Name(s): Egghe, L.
Language: English
Document Type: Article

Author Keywords: h-index; Lotka; g-index; R-index; Randic; pi-index
KeyWords Plus: CITATION DISTRIBUTIONS; SCIENTIFIC PUBLICATION; HIRSCH-
INDEX; COMPETITION; MODEL

Abstract: In a Lotkaian framework there exist formulae for impact measures 
such as the h-index, g-index, R-index and Randic'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 Randic with the total number of 
papers. In all cases we have a decreasing 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 pi-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 pi- or root pi-index. (C) 2010 Elsevier Ltd. All rights reserved.

Addresses: [Egghe, L.] Univ Antwerp, B-2000 Antwerp, Belgium; [Egghe, L.] 
Univ Hasselt UHasselt, B-3590 Diepenbeek, Belgium
Reprint Address: Egghe, L, Univ Antwerp, Stadscampus,Venusstr 35, B-2000 
Antwerp, Belgium.

E-mail Address: leo.egghe at uhasselt.be
ISSN: 0895-7177
DOI: 10.1016/j.mcm.2010.09.012
URL (not open access): http://dx.doi.org/10.1016/j.mcm.2010.09.012