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

Author

Listed:
  • Mark Levene

    (University of London)

  • Trevor Fenner

    (University of London)

  • Judit Bar-Ilan

    (Bar-Ilan University)

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.

Suggested Citation

  • Mark Levene & Trevor Fenner & Judit Bar-Ilan, 2019. "Characterisation of the $$\chi$$χ-index and the rec-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 120(2), pages 885-896, August.
    • Handle: RePEc:spr:scient:v:120:y:2019:i:2:d:10.1007_s11192-019-03151-7
    DOI: 10.1007/s11192-019-03151-7
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    References listed on IDEAS

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    1. Mark Levene & Martyn Harris & Trevor Fenner, 2020. "A two-dimensional bibliometric index reflecting both quality and quantity," Scientometrics, Springer;Akadémiai Kiadó, vol. 123(3), pages 1235-1246, June.

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