Advertisement

Power-Law Citation Distributions are Not Scale-Free

  • Michael Golosovsky
Chapter
  • 254 Downloads
Part of the SpringerBriefs in Complexity book series (BRIEFSCOMPLEXITY)

Abstract

We analyze time evolution of statistical distributions of citations to scientific papers published in the same year. While these distributions seem to follow the power-law dependence, we find that they are nonstationary and the exponent of the power-law fit decreases with time and does not come to saturation. We attribute the nonstationarity of citation distributions to different longevity of the low-cited and highly-cited papers. By measuring citation trajectories of papers, we found that citation careers of the low-cited papers come to saturation after 10–15 years while those of the highly-cited papers continue to increase indefinitely. When the number of citations of a paper exceeds some citation threshold, it becomes a runaway. Thus, we show that although citation distribution can look as a power-law dependence, it is not scale-free and there is a hidden dynamic scale associated with the onset of runaways. We show that our model of citation dynamics based on copying/redirection/triadic closure accounts for these issues fairly well.

Keywords

Power law distribution Scale-free distribution Citation lifetime 

References

  1. 2.
    Albarrán, P., Crespo, J. A., Ortuño, I., & Ruiz-Castillo, J. (2011). The skewness of science in 219 sub-fields and a number of aggregates. Scientometrics, 88(2), 385–397.CrossRefGoogle Scholar
  2. 3.
    Albert, R., & Barabasi, A. L. (2002). Statistical mechanics of complex networks. Reviews of Modern Physics, 74, 47–97.ADSMathSciNetCrossRefGoogle Scholar
  3. 7.
    Barabasi, A. L. (2015). Network science. Cambridge: Cambridge University Press.zbMATHGoogle Scholar
  4. 10.
    Baumgartner, S. E., & Leydesdorff L. (2013). Group-based trajectory modeling (GBTM) of citations in scholarly literature: Dynamic qualities of “transient” and “sticky knowledge claims”. Journal of the Association for Information Science and Technology, 65(4), 797–811.CrossRefGoogle Scholar
  5. 14.
    Bianconi, G., & Barabasi, A.-L. (2001). Bose-Einstein condensation in complex networks. Physical Review Letters, 86, 5632–5635.ADSCrossRefGoogle Scholar
  6. 22.
    Broido, A. D., & Clauset, A. (2019). Scale-free networks are rare. Nature Communications, 10(1), 1017.ADSCrossRefGoogle Scholar
  7. 24.
    Brzezinski, M. (2015). Power laws in citation distributions: evidence from Scopus. Scientometrics, 103(1), 213–228.MathSciNetCrossRefGoogle Scholar
  8. 26.
    Burrell, Q. L. (2005). The use of the generalized Waring process in modelling informetric data. Scientometrics, 64(3), 247–270.CrossRefGoogle Scholar
  9. 28.
    Caldarelli, G. (2007). Scale-free networks: Complex webs in nature and technology. Oxford: Oxford University Press.CrossRefGoogle Scholar
  10. 41.
    Clauset, A., Shalizi, C., & Newman, M. (2009). Power-law distributions in empirical data. SIAM Review, 51(4), 661–703.ADSMathSciNetCrossRefGoogle Scholar
  11. 44.
    Csárdi, G., Strandburg, K. J., Zalányi, L., Tobochnik, J., & Érdi, P. (2007). Modeling innovation by a kinetic description of the patent citation system. Physica A: Statistical Mechanics and Its Applications, 374(2), 783–793.ADSCrossRefGoogle Scholar
  12. 45.
    de Solla Price, D. J. (1965). Networks of scientific papers. Science, 149(3683), 510–515.ADSCrossRefGoogle Scholar
  13. 48.
    Dorogovtsev, S. N., & Mendes, J. F. F. (2001). Scaling properties of scale-free evolving networks: Continuous approach. Physical Review E, 63(5), 056125.ADSCrossRefGoogle Scholar
  14. 51.
    Evans, T. S., Hopkins, N., & Kaube, B. S. (2012). Universality of performance indicators based on citation and reference counts. Scientometrics, 93(2), 473–495.CrossRefGoogle Scholar
  15. 63.
    Glanzel, W. (2004). Towards a model for diachronous and synchronous citation analyses. Scientometrics, 60(3), 511–522.CrossRefGoogle Scholar
  16. 67.
    Golosovsky, M. (2017). Power-law citation distributions are not scale-free. Physical Review E, 96(3), 032306.ADSCrossRefGoogle Scholar
  17. 69.
    Golosovsky, M., & Solomon, S. (2012). Runaway events dominate the heavy tail of citation distributions. The European Physical Journal, 205(1), 303–311.ADSGoogle Scholar
  18. 76.
    Higham, K. W., Governale, M., Jaffe, A. B., & Zülicke, U. (2017). Fame and obsolescence: Disentangling growth and aging dynamics of patent citations. Physical Review E, 95(4), 042309.ADSCrossRefGoogle Scholar
  19. 87.
    Kong, J. S., Sarshar, N., & Roychowdhury, V. P. (2008). Experience versus talent shapes the structure of the Web. Proceedings of the National Academy of Sciences, 105(37), 13724–13729.ADSCrossRefGoogle Scholar
  20. 88.
    Krapivsky, P. L., & Redner, S. (2001). Organization of growing random networks. Physical Review E, 63(6), 066123.ADSCrossRefGoogle Scholar
  21. 94.
    Lehmann, S., Jackson, A. D., & Lautrup, B. (2005). Life, death and preferential attachment. Europhysics Letters, 69(2), 298–303.ADSCrossRefGoogle Scholar
  22. 97.
    Leskovec, J., Kleinberg, J., & Faloutsos, C. (2007). Graph evolution: Densification and shrinking diameters. ACM Transactions on Knowledge Discovery from Data (TKDD), 1(1), 2.CrossRefGoogle Scholar
  23. 102.
    Limpert, E., Stahel, W. A., & Abbt, M. (2001). Log-normal distributions across the sciences: Keys and clues. BioScience, 51(5), 341–352.CrossRefGoogle Scholar
  24. 111.
    Mingers, J., & Burrell, Q. L. (2006). Modeling citation behavior in Management Science journals. Information Processing & Management, 42(6), 1451–1464.CrossRefGoogle Scholar
  25. 114.
    Mitzenmacher, M. (2004). A brief history of generative models for power law and lognormal distributions. Internet Mathematics, 1(2), 226–251.MathSciNetCrossRefGoogle Scholar
  26. 115.
    Mitzenmacher, M. (2005). Editorial: The future of power law research. Internet Mathematics, 2(4), 525–534.CrossRefGoogle Scholar
  27. 117.
    Mokryn, O., & Reznik, A. (2015). On skewed distributions and straight lines. In Proceedings of the 24th International Conference on World Wide Web. New York, NY: Association for Computing Machinery.Google Scholar
  28. 123.
    Newman, M. E. (2005). Power Laws, Pareto distributions and Zipf’s law. Contemporary Physics, 46(5), 323–351.ADSCrossRefGoogle Scholar
  29. 136.
    Pinto, C. M. A., Lopes, A. M., & Machado, J. A. T. (2012). A review of power laws in real life phenomena. Communications in Nonlinear Science and Numerical Simulation, 17(9), 3558–3578.ADSMathSciNetCrossRefGoogle Scholar
  30. 142.
    Redner, S. (1998). How popular is your paper? An empirical study of the citation distribution. The European Physical Journal B, 4(2), 131–134.ADSCrossRefGoogle Scholar
  31. 144.
    Redner, S. (2005). Citation statistics from 110 years of Physical Review. Physics Today, 58(6), 49–54.CrossRefGoogle Scholar
  32. 158.
    Sornette, D. (2012). Probability distributions in complex systems. In Computational complexity (pp. 2286–2300). New York, NY: Springer.CrossRefGoogle Scholar
  33. 160.
    Stringer, M. J., Sales-Pardo, M., & Amaral, L. A. N. (2008). Effectiveness of journal ranking schemes as a tool for locating information. PLoS One, 3(2), e1683.ADSCrossRefGoogle Scholar
  34. 161.
    Stumpf, M. P. H., & Porter, M. A. (2012). Critical truths about power laws. Science, 335(6069), 665–666.ADSMathSciNetCrossRefGoogle Scholar
  35. 165.
    Thelwall, M. (2016). The discretised lognormal and hooked power law distributions for complete citation data: Best options for modelling and regression. Journal of Informetrics, 10(2), 336–346.CrossRefGoogle Scholar
  36. 172.
    Vazquez, A. (2003). Growing network with local rules: Preferential attachment, clustering hierarchy, and degree correlations. Physical Review E, 67, 056104.ADSCrossRefGoogle Scholar
  37. 177.
    Willinger, W., Alderson, D., & Doyle, J. C. (2009). Mathematics and the Internet: A source of enormous confusion and great potential. Notices of the AMS, 56(5), 586–599.MathSciNetzbMATHGoogle Scholar
  38. 186.
    Zhou, S., & Mondragon. R. J. (2004). Accurately modeling the internet topology. Physical Review E, 70, 066108.ADSCrossRefGoogle Scholar

Copyright information

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Michael Golosovsky
    • 1
  1. 1.Racah Institute of PhysicsHebrew University of JerusalemJerusalemIsrael

Personalised recommendations