IDEAS home Printed from https://ideas.repec.org/a/spr/scient/v120y2019i2d10.1007_s11192-019-03151-7.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11192-019-03151-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11192-019-03151-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bornmann, Lutz & Mutz, Rüdiger & Hug, Sven E. & Daniel, Hans-Dieter, 2011. "A multilevel meta-analysis of studies reporting correlations between the h index and 37 different h index variants," Journal of Informetrics, Elsevier, vol. 5(3), pages 346-359.
    2. Bouyssou, Denis & Marchant, Thierry, 2014. "An axiomatic approach to bibliometric rankings and indices," Journal of Informetrics, Elsevier, vol. 8(3), pages 449-477.
    3. Bouyssou, Denis & Marchant, Thierry, 2016. "Ranking authors using fractional counting of citations: An axiomatic approach," Journal of Informetrics, Elsevier, vol. 10(1), pages 183-199.
    4. Leo Egghe, 2006. "Theory and practise of the g-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 69(1), pages 131-152, October.
    5. Motty Perry & Philip J. Reny, 2016. "How to Count Citations If You Must," American Economic Review, American Economic Association, vol. 106(9), pages 2722-2741, September.
    6. Jevin D. West & Michael C. Jensen & Ralph J. Dandrea & Gregory J. Gordon & Carl T. Bergstrom, 2013. "Author‐level Eigenfactor metrics: Evaluating the influence of authors, institutions, and countries within the social science research network community," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 64(4), pages 787-801, April.
    7. Fiala, Dalibor & Šubelj, Lovro & Žitnik, Slavko & Bajec, Marko, 2015. "Do PageRank-based author rankings outperform simple citation counts?," Journal of Informetrics, Elsevier, vol. 9(2), pages 334-348.
    8. Kongo, Takumi, 2014. "An alternative axiomatization of the Hirsch index," Journal of Informetrics, Elsevier, vol. 8(1), pages 252-258.
    9. Lorna Wildgaard & Jesper W. Schneider & Birger Larsen, 2014. "A review of the characteristics of 108 author-level bibliometric indicators," Scientometrics, Springer;Akadémiai Kiadó, vol. 101(1), pages 125-158, October.
    10. Quesada, Antonio, 2011. "Axiomatics for the Hirsch index and the Egghe index," Journal of Informetrics, Elsevier, vol. 5(3), pages 476-480.
    11. Thierry Marchant, 2009. "An axiomatic characterization of the ranking based on the h-index and some other bibliometric rankings of authors," Scientometrics, Springer;Akadémiai Kiadó, vol. 80(2), pages 325-342, August.
    12. Antonio Quesada, 2011. "Further characterizations of the Hirsch index," Scientometrics, Springer;Akadémiai Kiadó, vol. 87(1), pages 107-114, April.
    13. Woeginger, Gerhard J., 2008. "A symmetry axiom for scientific impact indices," Journal of Informetrics, Elsevier, vol. 2(4), pages 298-303.
    14. Filippo Radicchi & Claudio Castellano, 2013. "Analysis of bibliometric indicators for individual scholars in a large data set," Scientometrics, Springer;Akadémiai Kiadó, vol. 97(3), pages 627-637, December.
    15. Subochev, Andrey & Aleskerov, Fuad & Pislyakov, Vladimir, 2018. "Ranking journals using social choice theory methods: A novel approach in bibliometrics," Journal of Informetrics, Elsevier, vol. 12(2), pages 416-429.
    16. Trevor Fenner & Martyn Harris & Mark Levene & Judit Bar-Ilan, 2018. "A novel bibliometric index with a simple geometric interpretation," PLOS ONE, Public Library of Science, vol. 13(7), pages 1-14, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Osório, António (António Miguel), 2019. "The value and credits of n-authors publications," Working Papers 2072/376026, Universitat Rovira i Virgili, Department of Economics.
    2. Csató, László, 2019. "Journal ranking should depend on the level of aggregation," Journal of Informetrics, Elsevier, vol. 13(4).
    3. Ana Paula dos Santos Rubem & Ariane Lima Moura & João Carlos Correia Baptista Soares de Mello, 2015. "Comparative analysis of some individual bibliometric indices when applied to groups of researchers," Scientometrics, Springer;Akadémiai Kiadó, vol. 102(1), pages 1019-1035, January.
    4. L'aszl'o Csat'o, 2019. "Journal ranking should depend on the level of aggregation," Papers 1904.06300, arXiv.org, revised Sep 2019.
    5. Bouyssou, Denis & Marchant, Thierry, 2016. "Ranking authors using fractional counting of citations: An axiomatic approach," Journal of Informetrics, Elsevier, vol. 10(1), pages 183-199.
    6. Bouyssou, Denis & Marchant, Thierry, 2014. "An axiomatic approach to bibliometric rankings and indices," Journal of Informetrics, Elsevier, vol. 8(3), pages 449-477.
    7. Sylvain Béal & Eric Rémila & Philippe Solal & Sylvain Ferrières, 2016. "An axiomatization of the iterated h-index and applications to sport rankings," Working Papers hal-01394818, HAL.
    8. Brandão, Luana Carneiro & Soares de Mello, João Carlos Correia Baptista, 2019. "A multi-criteria approach to the h-index," European Journal of Operational Research, Elsevier, vol. 276(1), pages 357-363.
    9. Josep Freixas & Roger Hoerl & William S. Zwicker, 2023. "Nash's bargaining problem and the scale-invariant Hirsch citation index," Papers 2309.01192, arXiv.org.
    10. László Csató & Dóra Gréta Petróczy, 2024. "Bibliometric indices as a measure of performance and competitive balance in the knockout stage of the UEFA Champions League," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 32(4), pages 961-988, December.
    11. 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.
    12. Antonin Mac'e, 2017. "The Limits of Citation Counts," Papers 1711.02695, arXiv.org, revised Sep 2023.
    13. Antonin Macé, 2023. "The Limits of Citation Counts," Working Papers halshs-01630095, HAL.
    14. Chambers, Christopher P. & Miller, Alan D., 2014. "Scholarly influence," Journal of Economic Theory, Elsevier, vol. 151(C), pages 571-583.
    15. Haley, M. Ryan & McGee, M. Kevin, 2020. "Jointly valuing journal visibility and author citation count: An axiomatic approach," Journal of Informetrics, Elsevier, vol. 14(1).
    16. Conan Mukherjee & Ranojoy Basu & Aftab Alam, 2020. "A measure of authorship by publications," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 41(3), pages 354-361, April.
    17. Adachi, Tsuyoshi & Kongo, Takumi, 2015. "Further axiomatizations of Egghe's g-index," Journal of Informetrics, Elsevier, vol. 9(4), pages 839-844.
    18. Woeginger, Gerhard J., 2014. "Investigations on the step-based research indices of Chambers and Miller," Journal of Informetrics, Elsevier, vol. 8(3), pages 659-666.
    19. Nadia Simoes & Nuno Crespo, 2020. "A flexible approach for measuring author-level publishing performance," Scientometrics, Springer;Akadémiai Kiadó, vol. 122(1), pages 331-355, January.
    20. Lathabai, Hiran H., 2020. "ψ-index: A new overall productivity index for actors of science and technology," Journal of Informetrics, Elsevier, vol. 14(4).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:scient:v:120:y:2019:i:2:d:10.1007_s11192-019-03151-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.