Characterisation of the χ -index and the rec-index

Mark Levene, Trevor Fenner, Judit Bar-Ilan

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 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 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.

Original languageEnglish
Pages (from-to)885-896
Number of pages12
Issue number2
StatePublished - 15 Aug 2019

Bibliographical note

Publisher Copyright:
© 2019, Akadémiai Kiadó, Budapest, Hungary.


  • Axiomatic characterisation
  • Bibliometric index
  • Core publications
  • Quantity versus quality
  • h-index
  • rec-index
  • χ-index


Dive into the research topics of 'Characterisation of the χ -index and the rec-index'. Together they form a unique fingerprint.

Cite this