A two-dimensional bibliometric index reflecting both quality and quantity

Abstract

We propose a two-dimensional bibliometric index that strikes a balance between quantity (as measured by the number of publications of a researcher) and quality (as measured by the number of citations to those publications). While the square of h-index is determined by the maximum area square that fits under the citation curve of an author when plotting the number of citations in decreasing order, the rec-index is determined by the maximum area rectangle that fits under the curve. In this context we may distinguish between authors with a few very highly-cited publications, who may have carried out some influential research, and prolific authors, who may have many publications but fewer citations per publication. The influence of a researcher may be measured via a restricted version of the rec-index, the ${rec}_{I}$-index, which is the maximum area vertical rectangle that fits under the citation curve. Similarly, the prolificity of a researcher may be measured via the ${rec}_{P}$-index, which is the maximum area horizontal rectangle that fits under the citation curve. This leads to the proposal of the two-dimensional bibliometric index $({rec}_{I}, {rec}_{P})$, which captures both aspects of a researcher’s output. We present a comprehensive empirical analysis of this two-dimensional index on two datasets: a large set of Google Scholar profiles (representing “typical” researchers) and a small set of Nobel prize winners. Our results demonstrate the potential of this two-dimensional index, since for both data sets there is a statistically significant number of researchers for whom ${rec}_{I}$ is greater than ${rec}_{P}$. In particular, for nearly 25% of the Google Scholar researchers and for nearly 60% of the Nobel prize winners, ${rec}_{I}$ is greater than ${rec}_{P}$.