Characterisation of the $$\chi$$χ-index and the rec-index

Mark Levene (), Trevor Fenner () and Judit Bar-Ilan ()
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Mark Levene: University of London
Trevor Fenner: University of London
Judit Bar-Ilan: Bar-Ilan University

Scientometrics, 2019, vol. 120, issue 2, No 24, 885-896

Abstract: Abstract Axiomatic characterisation of a bibliometric index provides insight into the properties that the index satisfies and facilitates the comparison of different indices. A geometric generalisation of the h-index, called the $$\chi$$χ-index, has recently been proposed to address some of the problems with the h-index, in particular, the fact that it is not scale invariant, i.e., multiplying the number of citations of each publication by a positive constant may change the relative ranking of two researchers. While the square of the h-index is the area of the largest square under the citation curve of a researcher, the square of the $$\chi$$χ-index, which we call the rec-index (or rectangle-index), is the area of the largest rectangle under the citation curve. Our main contribution here is to provide a characterisation of the rec-index via three properties: monotonicity, uniform citation and uniform equivalence. Monotonicity is a natural property that we would expect any bibliometric index to satisfy, while the other two properties constrain the value of the rec-index to be the area of the largest rectangle under the citation curve. The rec-index also allows us to distinguish between influential researchers who have relatively few, but highly-cited, publications and prolific researchers who have many, but less-cited, publications.

Keywords: h-index; $$\chi$$ χ -index; rec-index; Bibliometric index; Core publications; Quantity versus quality; Axiomatic characterisation (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11192-019-03151-7

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