Comprehensive evaluation of h-index and its extensions in the domain of mathematics

Until the late 90’s, conventional bibliometric indices such as, publication count, citation count, and number of co-authors have extensively been employed by the scientific community to rank the researchers. In 2005, inception of a renowned ranking measure h-index has grabbed the substantial importance; the community considered h-index as a quintessential ranking measure. Subsequently, different variants and extensions of h-index have also been proposed. To date, plethora of the studies exists that harnesses h-index, its variants and extensions for researchers’ ranking. Nonetheless, the community does not agree upon a single measure that can be deemed as an optimal ranking measure. This is due to the fact that most of the contemporary studies have evaluated them either by employing a small amount of data or presumed their significance on the basis of hypothetical or imaginary case scenarios. We argue that comprehensive empirical investigation of these measures must be performed in order to tackle their real behavior. This study evaluates the h-index and its extensions by employing a comprehensive data set of authors from Mathematics discipline. The first experimental step involves the computation of correlation among the obtained values of the extensions to determine the similarity and divergence among them. Afterwards, we considered the data of international award winners from four prestigious Mathematics societies as benchmark to validate the potential of these measures by analyzing the dependence of societies on them. The outcomes revealed that overall 45% of the authors have appeared at the top occurrences of the ranked list. Out of all extensions, fraction count on paper has outperformed by bringing 55% of the awardees at top 10% of its ranked list.