IDEAS home Printed from https://ideas.repec.org/a/spr/scient/v126y2021i7d10.1007_s11192-020-03699-9.html
   My bibliography  Save this article

The h-index formalism

Author

Listed:
  • Leo Egghe

    (University of Hasselt)

  • Ronald Rousseau

    (University of Antwerp
    KU Leuven)

Abstract

This article provides an overview of the development of the h-index formalism. We begin with the original formulation as provided by Hirsch and move on to the latest versions. In this we show how the h-index formalism has evolved over time. Lesser known versions, in particular the continuous version of the h-index is brought to the front. We also discuss the Prathap–Kosmulski–Schubert successive h-indices. As announced in the title we focus on the h-index formalism, omitting generalizations, such as the g-index, and applications in research assessment.

Suggested Citation

  • Leo Egghe & Ronald Rousseau, 2021. "The h-index formalism," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(7), pages 6137-6145, July.
    • Handle: RePEc:spr:scient:v:126:y:2021:i:7:d:10.1007_s11192-020-03699-9
    DOI: 10.1007/s11192-020-03699-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11192-020-03699-9
    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/s11192-020-03699-9?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. Dilruba Mahbuba & Ronald Rousseau, 2013. "Year-based h-type indicators," Scientometrics, Springer;Akadémiai Kiadó, vol. 96(3), pages 785-797, September.
    2. Leo Egghe & Ronald Rousseau, 2019. "A geometric relation between the h-index and the Lorenz curve," Scientometrics, Springer;Akadémiai Kiadó, vol. 119(2), pages 1281-1284, May.
    3. Denis Bouyssou & Thierry Marchant, 2011. "Ranking scientists and departments in a consistent manner," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 62(9), pages 1761-1769, September.
    4. van Eck, Nees Jan & Waltman, Ludo, 2008. "Generalizing the h- and g-indices," Journal of Informetrics, Elsevier, vol. 2(4), pages 263-271.
    5. Leo Egghe & Ronald Rousseau, 2006. "An informetric model for the Hirsch-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 69(1), pages 121-129, October.
    6. Ludo Waltman & Nees Jan van Eck, 2012. "The inconsistency of the h‐index," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 63(2), pages 406-415, February.
    7. Ronald Rousseau, 2016. "Citation data as a proxy for quality or scientific influence are at best PAC (probably approximately correct)," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 67(12), pages 3092-3094, December.
    8. Anthony F. J. Raan, 2006. "Comparison of the Hirsch-index with standard bibliometric indicators and with peer judgment for 147 chemistry research groups," Scientometrics, Springer;Akadémiai Kiadó, vol. 67(3), pages 491-502, June.
    9. Leo Egghe, 2008. "Modelling successive h-indices," Scientometrics, Springer;Akadémiai Kiadó, vol. 77(3), pages 377-387, December.
    10. András Schubert, 2007. "Successive h-indices," Scientometrics, Springer;Akadémiai Kiadó, vol. 70(1), pages 201-205, January.
    11. E. Garfield & I. H. Sher, 1963. "New factors in the evaluation of scientific literature through citation indexing," American Documentation, Wiley Blackwell, vol. 14(3), pages 195-201, July.
    12. Yuxian Liu & Ronald Rousseau, 2009. "Properties of Hirsch-type indices: the case of library classification categories," Scientometrics, Springer;Akadémiai Kiadó, vol. 79(2), pages 235-248, May.
    13. Egghe, Leo & Rousseau, Ronald, 2019. "Solution by step functions of a minimum problem in L2[0,T], using generalized h- and g-indices," Journal of Informetrics, Elsevier, vol. 13(3), pages 785-792.
    14. Michael G. Banks, 2006. "An extension of the Hirsch index: Indexing scientific topics and compounds," Scientometrics, Springer;Akadémiai Kiadó, vol. 69(1), pages 161-168, October.
    15. Egghe, Leo & Rousseau, Ronald, 2020. "Polar coordinates and generalized h-type indices," Journal of Informetrics, Elsevier, vol. 14(2).
    16. Egghe, Leo & Rousseau, Ronald, 2019. "Infinite sequences and their h-type indices," Journal of Informetrics, Elsevier, vol. 13(1), pages 291-298.
    17. Ludo Waltman & Nees Jan van Eck, 2012. "The inconsistency of the h-index," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 63(2), pages 406-415, February.
    18. van Eck, N.J.P. & Waltman, L., 2008. "Generalizing the h- and g-indices," ERIM Report Series Research in Management ERS-2008-049-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    19. Tibor Braun & Wolfgang Glänzel & András Schubert, 2006. "A Hirsch-type index for journals," Scientometrics, Springer;Akadémiai Kiadó, vol. 69(1), pages 169-173, October.
    20. Edit Csajbók & Anna Berhidi & Lívia Vasas & András Schubert, 2007. "Hirsch-index for countries based on Essential Science Indicators data," Scientometrics, Springer;Akadémiai Kiadó, vol. 73(1), pages 91-117, October.
    21. Alonso, S. & Cabrerizo, F.J. & Herrera-Viedma, E. & Herrera, F., 2009. "h-Index: A review focused in its variants, computation and standardization for different scientific fields," Journal of Informetrics, Elsevier, vol. 3(4), pages 273-289.
    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. Chen, Meiqian & Guo, Zhaoxia & Dong, Yucheng & Chiclana, Francisco & Herrera-Viedma, Enrique, 2021. "Citations optimal growth path: A tool to analyze sensitivity to citations of h-like indexes," Journal of Informetrics, Elsevier, vol. 15(4).
    2. Biró, Tamás S. & Telcs, András & Józsa, Máté & Néda, Zoltán, 2023. "Gintropic scaling of scientometric indexes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    3. Egghe, Leo, 2021. "A theory of pointwise defined impact measures," Journal of Informetrics, Elsevier, vol. 15(3).
    4. Marek Gagolewski & Barbara Żogała-Siudem & Grzegorz Siudem & Anna Cena, 2022. "Ockham’s index of citation impact," Scientometrics, Springer;Akadémiai Kiadó, vol. 127(5), pages 2829-2845, May.
    5. Cena, Anna & Gagolewski, Marek & Siudem, Grzegorz & Żogała-Siudem, Barbara, 2022. "Validating citation models by proxy indices," Journal of Informetrics, Elsevier, vol. 16(2).

    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. Leo Egghe & Ronald Rousseau, 2020. "Minimal Impact One-Dimensional Arrays," Mathematics, MDPI, vol. 8(5), pages 1-11, May.
    2. Alonso, S. & Cabrerizo, F.J. & Herrera-Viedma, E. & Herrera, F., 2009. "h-Index: A review focused in its variants, computation and standardization for different scientific fields," Journal of Informetrics, Elsevier, vol. 3(4), pages 273-289.
    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. Bouyssou, Denis & Marchant, Thierry, 2014. "An axiomatic approach to bibliometric rankings and indices," Journal of Informetrics, Elsevier, vol. 8(3), pages 449-477.
    5. Deming Lin & Tianhui Gong & Wenbin Liu & Martin Meyer, 2020. "An entropy-based measure for the evolution of h index research," Scientometrics, Springer;Akadémiai Kiadó, vol. 125(3), pages 2283-2298, December.
    6. Leo Egghe & Ronald Rousseau, 2019. "Measures of linear type lead to a characterization of Zipf functions," Scientometrics, Springer;Akadémiai Kiadó, vol. 121(3), pages 1707-1715, December.
    7. John Panaretos & Chrisovaladis Malesios, 2009. "Assessing scientific research performance and impact with single indices," Scientometrics, Springer;Akadémiai Kiadó, vol. 81(3), pages 635-670, December.
    8. 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.
    9. Bornmann, Lutz & Marx, Werner, 2012. "HistCite analysis of papers constituting the h index research front," Journal of Informetrics, Elsevier, vol. 6(2), pages 285-288.
    10. 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.
    11. Wei, Shelia X. & Tong, Tong & Rousseau, Ronald & Wang, Wanru & Ye, Fred Y., 2022. "Relations among the h-, g-, ψ-, and p-index and offset-ability," Journal of Informetrics, Elsevier, vol. 16(4).
    12. Egghe, Leo, 2021. "A theory of pointwise defined impact measures," Journal of Informetrics, Elsevier, vol. 15(3).
    13. Leo Egghe, 2009. "Performance and its relation with productivity in Lotkaian systems," Scientometrics, Springer;Akadémiai Kiadó, vol. 81(2), pages 567-585, November.
    14. Hyeonchae Yang & Woo-Sung Jung, 2015. "A strategic management approach for Korean public research institutes based on bibliometric investigation," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(4), pages 1437-1464, July.
    15. Maziar Montazerian & Edgar Dutra Zanotto & Hellmut Eckert, 2019. "A new parameter for (normalized) evaluation of H-index: countries as a case study," Scientometrics, Springer;Akadémiai Kiadó, vol. 118(3), pages 1065-1078, March.
    16. Marcin Kozak & Lutz Bornmann, 2012. "A New Family of Cumulative Indexes for Measuring Scientific Performance," PLOS ONE, Public Library of Science, vol. 7(10), pages 1-4, October.
    17. Yang, Alex Jie & Wu, Linwei & Zhang, Qi & Wang, Hao & Deng, Sanhong, 2023. "The k-step h-index in citation networks at the paper, author, and institution levels," Journal of Informetrics, Elsevier, vol. 17(4).
    18. Egghe, Leo & Rousseau, Ronald, 2020. "Polar coordinates and generalized h-type indices," Journal of Informetrics, Elsevier, vol. 14(2).
    19. 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.
    20. Zhang, Lin & Thijs, Bart & Glänzel, Wolfgang, 2011. "The diffusion of H-related literature," Journal of Informetrics, Elsevier, vol. 5(4), pages 583-593.

    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:126:y:2021:i:7:d:10.1007_s11192-020-03699-9. 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.