Real and rational variants of the h-index and the g-index

Abstract

The definitions of the rational and real-valued variants of the h-index and g-index are reviewed. It is shown how they can be obtained both graphically and by calculation. Formulae are derived expressing the exact relations between the h-variants and between the g-variants. Subsequently these relations are examined. In a citation context the real h-index is often, but not always, smaller than the rational h-index. It is also shown that the relation between the real and the rational g-index depends on the number of citations of the article ranked g + 1. Maximum differences between h, h(r) and h(rat) on the one hand and between g, g(r) and g(rat) on the other are determined. (C) 2008 Elsevier Ltd. All rights reserved.