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Citation graph, weighted impact factors and performance indices


  • Karol Życzkowski

    (Jagiellonian University
    Polska Akademia Nauk)


A scheme of evaluating an impact of a given scientific paper based on importance of papers quoting it is investigated. Introducing a weight of a given citation, dependent on the previous scientific achievements of the author of the citing paper, we define the weighting factor of a given scientist. Technically the weighting factors are defined by the components of the normalized leading eigenvector of the matrix describing the citation graph. The weighting factor of a given scientist, reflecting the scientific output of other researchers quoting his work, allows us to define weighted number of citation of a given paper, weighted impact factor of a journal and weighted Hirsch index of an individual scientist or of an entire scientific institution.

Suggested Citation

  • Karol Życzkowski, 2010. "Citation graph, weighted impact factors and performance indices," Scientometrics, Springer;Akadémiai Kiadó, vol. 85(1), pages 301-315, October.
  • Handle: RePEc:spr:scient:v:85:y:2010:i:1:d:10.1007_s11192-010-0208-6
    DOI: 10.1007/s11192-010-0208-6

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    References listed on IDEAS

    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. Benjamin M. Althouse & Jevin D. West & Carl T. Bergstrom & Theodore Bergstrom, 2009. "Differences in impact factor across fields and over time," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 60(1), pages 27-34, January.
    3. Aksnes, Dag W. & Rip, Arie, 2009. "Researchers' perceptions of citations," Research Policy, Elsevier, vol. 38(6), pages 895-905, July.
    4. Pablo D. Batista & Mônica G. Campiteli & Osame Kinouchi, 2006. "Is it possible to compare researchers with different scientific interests?," Scientometrics, Springer;Akadémiai Kiadó, vol. 68(1), pages 179-189, July.
    5. Frandsen, Tove Faber, 2007. "Journal self-citations—Analysing the JIF mechanism," Journal of Informetrics, Elsevier, vol. 1(1), pages 47-58.
    6. Woeginger, Gerhard J., 2008. "An axiomatic characterization of the Hirsch-index," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 224-232, September.
    7. 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.
    8. James H. Fowler & Dag W. Aksnes, 2007. "Does self-citation pay?," Scientometrics, Springer;Akadémiai Kiadó, vol. 72(3), pages 427-437, September.
    9. Chen, P. & Xie, H. & Maslov, S. & Redner, S., 2007. "Finding scientific gems with Google’s PageRank algorithm," Journal of Informetrics, Elsevier, vol. 1(1), pages 8-15.
    10. Wolfgang Glänzel & Koenraad Debackere & Bart Thijs & András Schubert, 2006. "A concise review on the role of author self-citations in information science, bibliometrics and science policy," Scientometrics, Springer;Akadémiai Kiadó, vol. 67(2), pages 263-277, May.
    11. András Schubert, 2007. "Successive h-indices," Scientometrics, Springer;Akadémiai Kiadó, vol. 70(1), pages 201-205, January.
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    Cited by:

    1. A. Ferrer-Sapena & E. A. Sánchez-Pérez & L. M. González & F. Peset & R. Aleixandre-Benavent, 2015. "Mathematical properties of weighted impact factors based on measures of prestige of the citing journals," Scientometrics, Springer;Akadémiai Kiadó, vol. 105(3), pages 2089-2108, December.
    2. Liwei Cai & Jiahao Tian & Jiaying Liu & Xiaomei Bai & Ivan Lee & Xiangjie Kong & Feng Xia, 2019. "Scholarly impact assessment: a survey of citation weighting solutions," Scientometrics, Springer;Akadémiai Kiadó, vol. 118(2), pages 453-478, February.
    3. Erjia Yan, 2014. "Topic-based Pagerank: toward a topic-level scientific evaluation," Scientometrics, Springer;Akadémiai Kiadó, vol. 100(2), pages 407-437, August.
    4. Hui Fang, 2020. "Investigating the journal impact along the columns and rows of the publication-citation matrix," Scientometrics, Springer;Akadémiai Kiadó, vol. 125(3), pages 2265-2282, December.
    5. Ludo Waltman & Erjia Yan & Nees Jan Eck, 2011. "A recursive field-normalized bibliometric performance indicator: an application to the field of library and information science," Scientometrics, Springer;Akadémiai Kiadó, vol. 89(1), pages 301-314, October.

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