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A novel bibliometric index with a simple geometric interpretation

Author

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  • Trevor Fenner
  • Martyn Harris
  • Mark Levene
  • Judit Bar-Ilan

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 k c k, 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

Suggested Citation

  • 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.
    • Handle: RePEc:plo:pone00:0200098
    DOI: 10.1371/journal.pone.0200098
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    Citations

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    Cited by:

    1. Shu-Chun Kuo & Tsair-Wei Chien & Willy Chou, 2022. "Suggestions to the article: medical professionalism research characteristics and hotspots," Scientometrics, Springer;Akadémiai Kiadó, vol. 127(2), pages 1191-1194, February.
    2. L'aszl'o Csat'o & D'ora Gr'eta Petr'oczy, 2020. "Bibliometric indices as a measure of performance and competitive balance in the knockout stage of the UEFA Champions League," Papers 2005.13416, arXiv.org, revised Sep 2023.
    3. 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.
    4. Shu-Chun Kuo & Yu-Tsen Yeh & Wei-Chih Kan & Tsair-Wei Chien, 2021. "The use of bootstrapping method to compare research achievements for ophthalmology authors in the US since 2010," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(1), pages 509-520, January.
    5. Corey J A Bradshaw & Justin M Chalker & Stefani A Crabtree & Bart A Eijkelkamp & John A Long & Justine R Smith & Kate Trinajstic & Vera Weisbecker, 2021. "A fairer way to compare researchers at any career stage and in any discipline using open-access citation data," PLOS ONE, Public Library of Science, vol. 16(9), pages 1-15, September.
    6. Maor Weinberger & Maayan Zhitomirsky-Geffet, 2021. "Diversity of success: measuring the scholarly performance diversity of tenured professors in the Israeli academia," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(4), pages 2931-2970, April.
    7. Shin-Yueh Liu & Tsair-Wei Chien & Ting-Ya Yang & Yu-Tsen Yeh & Willy Chou & Julie Chi Chow, 2021. "A Bibliometric Analysis on Dengue Outbreaks in Tropical and Sub-Tropical Climates Worldwide Since 1950," IJERPH, MDPI, vol. 18(6), pages 1-15, March.
    8. Ana León-Gómez & Jorge Alexander Mora Forero & Jose Manuel Santos-Jaén, 2023. "A Bibliometric Analysis of Sustainability Education in Tourism Universities," SAGE Open, , vol. 13(3), pages 21582440231, August.
    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. 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.
    11. Lin-Yen Wang & Tsair-Wei Chien & Willy Chou, 2021. "Using the IPcase Index with Inflection Points and the Corresponding Case Numbers to Identify the Impact Hit by COVID-19 in China: An Observation Study," IJERPH, MDPI, vol. 18(4), pages 1-16, February.
    12. 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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