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Mathematical theory of the h‐ and g‐index in case of fractional counting of authorship

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  • Leo Egghe

Abstract

This article studies the h‐index (Hirsch index) and the g‐index of authors, in case one counts authorship of the cited articles in a fractional way. There are two ways to do this: One counts the citations to these papers in a fractional way or one counts the ranks of the papers in a fractional way as credit for an author. In both cases, we define the fractional h‐ and g‐indexes, and we present inequalities (both upper and lower bounds) between these fractional h‐ and g‐indexes and their corresponding unweighted values (also involving, of course, the coauthorship distribution). Wherever applicable, examples and counterexamples are provided. In a concrete example (the publication citation list of the present author), we make explicit calculations of these fractional h‐ and g‐indexes and show that they are not very different from the unweighted ones.

Suggested Citation

  • Leo Egghe, 2008. "Mathematical theory of the h‐ and g‐index in case of fractional counting of authorship," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 59(10), pages 1608-1616, August.
    • Handle: RePEc:bla:jamist:v:59:y:2008:i:10:p:1608-1616
    DOI: 10.1002/asi.20845
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    Cited by:

    1. J. E. Hirsch, 2019. "hα: An index to quantify an individual’s scientific leadership," Scientometrics, Springer;Akadémiai Kiadó, vol. 118(2), pages 673-686, February.
    2. Fenghua Wang & Ying Fan & An Zeng & Zengru Di, 2019. "A nonlinear collective credit allocation in scientific publications," Scientometrics, Springer;Akadémiai Kiadó, vol. 119(3), pages 1655-1668, June.
    3. Péter Vinkler, 2023. "Impact of the number and rank of coauthors on h-index and π-index. The part-impact method," Scientometrics, Springer;Akadémiai Kiadó, vol. 128(4), pages 2349-2369, April.
    4. Muhammad Salman & Mohammad Masroor Ahmed & Muhammad Tanvir Afzal, 2021. "Assessment of author ranking indices based on multi-authorship," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(5), pages 4153-4172, May.
    5. Youssef Elomari & Masoud Norouzi & Marc Marín-Genescà & Alberto Fernández & Dieter Boer, 2022. "Integration of Solar Photovoltaic Systems into Power Networks: A Scientific Evolution Analysis," Sustainability, MDPI, vol. 14(15), pages 1-23, July.
    6. Kristina Galjanić & Ivan Marović & Nikša Jajac, 2022. "Decision Support Systems for Managing Construction Projects: A Scientific Evolution Analysis," Sustainability, MDPI, vol. 14(9), pages 1-23, April.
    7. Christoph Steinbrüchel, 2019. "A citation index for principal investigators," Scientometrics, Springer;Akadémiai Kiadó, vol. 118(1), pages 305-320, January.
    8. Loet Leydesdorff & Lutz Bornmann & Jonathan Adams, 2019. "The integrated impact indicator revisited (I3*): a non-parametric alternative to the journal impact factor," Scientometrics, Springer;Akadémiai Kiadó, vol. 119(3), pages 1669-1694, June.
    9. Anna Tietze & Philip Hofmann, 2019. "The h-index and multi-author hm-index for individual researchers in condensed matter physics," Scientometrics, Springer;Akadémiai Kiadó, vol. 119(1), pages 171-185, April.
    10. Simoes, Nadia & Crespo, Nuno, 2020. "Self-Citations and scientific evaluation: Leadership, influence, and performance," Journal of Informetrics, Elsevier, vol. 14(1).
    11. Siying Li & Huawei Shen & Peng Bao & Xueqi Cheng, 2021. "$$h_u$$ h u -index: a unified index to quantify individuals across disciplines," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(4), pages 3209-3226, April.
    12. Henry H. Bi, 2023. "Four problems of the h-index for assessing the research productivity and impact of individual authors," Scientometrics, Springer;Akadémiai Kiadó, vol. 128(5), pages 2677-2691, May.
    13. Lathabai, Hiran H., 2020. "ψ-index: A new overall productivity index for actors of science and technology," Journal of Informetrics, Elsevier, vol. 14(4).
    14. Crespo, Nuno & Simoes, Nadia, 2019. "Publication Performance and Number of Authors – Evidence for World Top Economists," MPRA Paper 92581, University Library of Munich, Germany.
    15. Tanmoy Konar, 2021. "Author-Suggested, Weighted Citation Index: A Novel Approach for Determining the Contribution of Individual Researchers," Publications, MDPI, vol. 9(3), pages 1-8, July.
    16. Rosenstreich, Daniela & Wooliscroft, Ben, 2009. "Measuring the impact of accounting journals using Google Scholar and the g-index," The British Accounting Review, Elsevier, vol. 41(4), pages 227-239.
    17. Rizwan Ghani & Faiza Qayyum & Muhammad Tanvir Afzal & Hermann Maurer, 2019. "Comprehensive evaluation of h-index and its extensions in the domain of mathematics," Scientometrics, Springer;Akadémiai Kiadó, vol. 118(3), pages 809-822, March.
    18. Gangan Prathap, 2021. "Letter to the editor: Dimensionless citation indicators for fractional counting," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(10), pages 8765-8769, October.

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