A novel bibliometric index with a simple geometric interpretation

Fenner, Trevor and Harris, Martyn and Levene, Mark and Bar-Ilan, J. (2018) A novel bibliometric index with a simple geometric interpretation. PLoS One , ISSN 1932-6203.

Abstract

We propose the χ-index as a bibliometric indicator that generalises the h-index. While the h-index is determined by the maximum square that fits under the citation curve of an author when plotting the number of citations in decreasing order, the χ-index is determined by the maximum area rectangle that fits under the curve. The height of the maximum rectangle is the number of citations ck to the kth most-cited publication, where k is the width of the rectangle. The χ-index is then defined as , for convenience of comparison with the h-index and other similar indices. We present a comprehensive empirical comparison between the χ-index and other bibliometric indices, focusing on a comparison with the h-index, by analysing two datasets—a large set of Google Scholar profiles and a small set of Nobel prize winners. Our results show that, although the χ and h indices are strongly correlated, they do exhibit significant differences. In particular, we show that, for these data sets, there are a substantial number of profiles for which χ is significantly larger than h. Furthermore, restricting these profiles to the cases when ck > k or ck < k corresponds to, respectively, classifying researchers as either tending to influential, i.e. having many more than h citations, or tending to prolific, i.e. having many more than h publications.

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