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Modeling a century of citation distributions

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  • Wallace, Matthew L.
  • Larivière, Vincent
  • Gingras, Yves

Abstract

The prevalence of uncited papers or of highly cited papers, with respect to the bulk of publications, provides important clues as to the dynamics of scientific research. Using 25 million papers and 600 million references from the Web of Science over the 1900–2006 period, this paper proposes a simple model based on a random selection process to explain the “uncitedness” phenomenon and its decline over the years. We show that the proportion of cited papers is a function of (1) the number of articles available (the competing papers), (2) the number of citing papers and (3) the number of references they contain. Using uncitedness as a departure point, we demonstrate the utility of the stretched-exponential function and a form of the Tsallis q-exponential function to fit complete citation distributions over the 20th century. As opposed to simple power-law fits, for instance, both these approaches are shown to be empirically well-grounded and robust enough to better understand citation dynamics at the aggregate level. On the basis of these models, we provide quantitative evidence and provisional explanations for an important shift in citation practices around 1960. We also propose a revision of the “citation classic” category as a set of articles which is clearly distinguishable from the rest of the field.

Suggested Citation

  • Wallace, Matthew L. & Larivière, Vincent & Gingras, Yves, 2009. "Modeling a century of citation distributions," Journal of Informetrics, Elsevier, vol. 3(4), pages 296-303.
  • Handle: RePEc:eee:infome:v:3:y:2009:i:4:p:296-303
    DOI: 10.1016/j.joi.2009.03.010
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    References listed on IDEAS

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    1. S. Redner, 1998. "How popular is your paper? An empirical study of the citation distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 4(2), pages 131-134, July.
    2. Gupta, Hari M. & Campanha, José R. & Schinaider, Sidney J., 2008. "Size limiting in Tsallis statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(27), pages 6745-6751.
    3. Mikhail V. Simkin & Vwani P. Roychowdhury, 2007. "A mathematical theory of citing," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 58(11), pages 1661-1673, September.
    4. Hendrik P. van Dalen & Kène Henkens, 2004. "Demographers and Their Journals: Who Remains Uncited After Ten Years?," Population and Development Review, The Population Council, Inc., vol. 30(3), pages 489-506, September.
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    Citations

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    Cited by:

    1. Pan, Raj K. & Petersen, Alexander M. & Pammolli, Fabio & Fortunato, Santo, 2018. "The memory of science: Inflation, myopia, and the knowledge network," Journal of Informetrics, Elsevier, vol. 12(3), pages 656-678.
    2. Thelwall, Mike, 2017. "Three practical field normalised alternative indicator formulae for research evaluation," Journal of Informetrics, Elsevier, vol. 11(1), pages 128-151.
    3. Wang, Jue & Zhang, Liwei, 2018. "Proximal advantage in knowledge diffusion: The time dimension," Journal of Informetrics, Elsevier, vol. 12(3), pages 858-867.
    4. Osterloh, Margit & Frey, Bruno S., 2020. "How to avoid borrowed plumes in academia," Research Policy, Elsevier, vol. 49(1).
    5. Liang, Liming & Zhong, Zhen & Rousseau, Ronald, 2015. "Uncited papers, uncited authors and uncited topics: A case study in library and information science," Journal of Informetrics, Elsevier, vol. 9(1), pages 50-58.
    6. Stegehuis, Clara & Litvak, Nelly & Waltman, Ludo, 2015. "Predicting the long-term citation impact of recent publications," Journal of Informetrics, Elsevier, vol. 9(3), pages 642-657.
    7. Lachance, Christian & Larivière, Vincent, 2014. "On the citation lifecycle of papers with delayed recognition," Journal of Informetrics, Elsevier, vol. 8(4), pages 863-872.
    8. Vîiu, Gabriel-Alexandru, 2018. "The lognormal distribution explains the remarkable pattern documented by characteristic scores and scales in scientometrics," Journal of Informetrics, Elsevier, vol. 12(2), pages 401-415.
    9. Copiello, Sergio, 2019. "Peer and neighborhood effects: Citation analysis using a spatial autoregressive model and pseudo-spatial data," Journal of Informetrics, Elsevier, vol. 13(1), pages 238-254.
    10. Phillips, J.C., 2015. "Phase transitions in the web of science," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 173-177.
    11. Thelwall, Mike & Sud, Pardeep, 2016. "National, disciplinary and temporal variations in the extent to which articles with more authors have more impact: Evidence from a geometric field normalised citation indicator," Journal of Informetrics, Elsevier, vol. 10(1), pages 48-61.
    12. Sangwal, Keshra, 2013. "Comparison of different mathematical functions for the analysis of citation distribution of papers of individual authors," Journal of Informetrics, Elsevier, vol. 7(1), pages 36-49.
    13. Ling-Ling Wu & Mu-Hsuan Huang & Ching-Yi Chen, 2012. "Citation patterns of the pre-web and web-prevalent environments: The moderating effects of domain knowledge," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 63(11), pages 2182-2194, November.
    14. Tol, Richard S.J., 2013. "The Matthew effect for cohorts of economists," Journal of Informetrics, Elsevier, vol. 7(2), pages 522-527.
    15. Thelwall, Mike, 2016. "Are the discretised lognormal and hooked power law distributions plausible for citation data?," Journal of Informetrics, Elsevier, vol. 10(2), pages 454-470.
    16. Bertoli-Barsotti, Lucio & Lando, Tommaso, 2015. "On a formula for the h-index," Journal of Informetrics, Elsevier, vol. 9(4), pages 762-776.
    17. González-Albo, Borja & Bordons, María, 2011. "Articles vs. proceedings papers: Do they differ in research relevance and impact? A case study in the Library and Information Science field," Journal of Informetrics, Elsevier, vol. 5(3), pages 369-381.
    18. Sangwal, Keshra, 2014. "Distributions of citations of papers of individual authors publishing in different scientific disciplines: Application of Langmuir-type function," Journal of Informetrics, Elsevier, vol. 8(4), pages 972-984.
    19. Roth, Camille & Wu, Jiang & Lozano, Sergi, 2012. "Assessing impact and quality from local dynamics of citation networks," Journal of Informetrics, Elsevier, vol. 6(1), pages 111-120.
    20. Phillips, J.C., 2013. "Self-organized criticality and color vision: A guide to water–protein landscape evolution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(3), pages 468-473.
    21. Sangwal, Keshra, 2013. "Citation and impact factor distributions of scientific journals published in individual countries," Journal of Informetrics, Elsevier, vol. 7(2), pages 487-504.

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