Theory and practise of the g-index

The g-index is introduced as an improvement of the h-index of Hirsch to measure the global citation performance of a set of articles. If this set is ranked in decreasing order of the number of citations that they received, the g-index is the (unique) largest number such that the top g articles received (together) at least g 2 citations. We prove the unique existence of g for any set of articles and we have that g ≥ h. The general Lotkaian theory of the g-index is presented and we show that g = (α-1 / α-2) α-1/α T 1/α where a> 2 is the Lotkaian exponent and where T denotes the total number of sources. We then present the g-index of the (still active) Price medallists for their complete careers up to 1972 and compare it with the h-index. It is shown that the g-index inherits all the good properties of the h-index and, in addition, better takes into account the citation scores of the top articles. This yields a better distinction between and order of the scientists from the point of view of visibility.

[1]  Philip Ball,et al.  Index aims for fair ranking of scientists , 2005, Nature.

[2]  Wolfgang Glänzel,et al.  H-Index for Price Medalists , 2005 .

[3]  Leo Egghe,et al.  Introduction to Informetrics: Quantitative Methods in Library, Documentation and Information Science , 1990 .

[4]  Paul Nicholls,et al.  Introduction to informetrics: Quantitative methods in library, documentation and information science , 1991 .

[5]  L. Egghe.  An improvement of the h-index: the g-index , 2006 .

[6]  Wolfgang Glänzel,et al.  A Hirsch-type index for journals , 2006, Scientometrics.

[7]  L. Egghe.  How to improve the h-index , 2006 .

[8]  L. Egghe.  Power Laws in the Information Production Process: Lotkaian Informetrics , 2005 .

[9]  I. K. Ravichandra Rao,et al.  Theory of first-citation distributions and applications , 2001 .

[10]  W. Glänzel,et al.  A Hirsch-type index for journals [1] , 2005 .

[11]  Leo Egghe,et al.  An informetric model for the Hirsch-index , 2006, Scientometrics.

[12]  Leo Egghe,et al.  Dynamic h-index: The Hirsch index in function of time , 2007, J. Assoc. Inf. Sci. Technol..

[13]  Wolfgang Glänzel,et al.  On the h-index - A mathematical approach to a new measure of publication activity and citation impact , 2006, Scientometrics.

[14]  Wolfgang Glänzel,et al.  On the Opportunities and Limitations of the H-index , 2006 .

[15]  J. E. Hirsch,et al.  An index to quantify an individual's scientific research output , 2005, Proc. Natl. Acad. Sci. USA.