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The power of power laws and an interpretation of Lotkaian informetric systems as self‐similar fractals

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  • L. Egghe

Abstract

Power laws as defined in 1926 by A. Lotka are increasing in importance because they have been found valid in varied social networks including the Internet. In this article some unique properties of power laws are proven. They are shown to characterize functions with the scale‐free property (also called self‐similarity property) as well as functions with the product property. Power laws have other desirable properties that are not shared by exponential laws, as we indicate in this paper. Specifically, Naranan (1970) proves the validity of Lotka's law based on the exponential growth of articles in journals and of the number of journals. His argument is reproduced here and a discrete‐time argument is also given, yielding the same law as that of Lotka. This argument makes it possible to interpret the information production process as a self‐similar fractal and show the relation between Lotka's exponent and the (self‐similar) fractal dimension of the system. Lotkaian informetric systems are self‐similar fractals, a fact revealed by Mandelbrot (1977) in relation to nature, but is also true for random texts, which exemplify a very special type of informetric system.

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  • L. Egghe, 2005. "The power of power laws and an interpretation of Lotkaian informetric systems as self‐similar fractals," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 56(7), pages 669-675, May.
    • Handle: RePEc:bla:jamist:v:56:y:2005:i:7:p:669-675
    DOI: 10.1002/asi.20158
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    Cited by:

    1. Koski, Timo & Sandström, Erik & Sandström, Ulf, 2016. "Towards field-adjusted production: Estimating research productivity from a zero-truncated distribution," Journal of Informetrics, Elsevier, vol. 10(4), pages 1143-1152.
    2. Mihail Cocosila & Alexander Serenko & Ofir Turel, 2011. "Exploring the management information systems discipline: a scientometric study of ICIS, PACIS and ASAC," Scientometrics, Springer;Akadémiai Kiadó, vol. 87(1), pages 1-16, April.
    3. Guillermo Armando Ronda-Pupo & J. Sylvan Katz, 2018. "The power law relationship between citation impact and multi-authorship patterns in articles in Information Science & Library Science journals," Scientometrics, Springer;Akadémiai Kiadó, vol. 114(3), pages 919-932, March.
    4. Torres-Salinas, Daniel & Rodríguez-Sánchez, Rosa & Robinson-García, Nicolás & Fdez-Valdivia, J. & García, J.A., 2013. "Mapping citation patterns of book chapters in the Book Citation Index," Journal of Informetrics, Elsevier, vol. 7(2), pages 412-424.
    5. Guillermo Armando Ronda-Pupo & Thong Pham, 2018. "The evolutions of the rich get richer and the fit get richer phenomena in scholarly networks: the case of the strategic management journal," Scientometrics, Springer;Akadémiai Kiadó, vol. 116(1), pages 363-383, July.
    6. Calabrese, Armando & Capece, Guendalina & Costa, Roberta & Di Pillo, Francesca & Giuffrida, Stefania, 2018. "A ‘power law’ based method to reduce size-related bias in indicators of knowledge performance: An application to university research assessment," Journal of Informetrics, Elsevier, vol. 12(4), pages 1263-1281.
    7. Bar-Ilan, Judit, 2008. "Informetrics at the beginning of the 21st century—A review," Journal of Informetrics, Elsevier, vol. 2(1), pages 1-52.
    8. Guillermo Armando Ronda-Pupo, 2017. "The citation-based impact of complex innovation systems scales with the size of the system," Scientometrics, Springer;Akadémiai Kiadó, vol. 112(1), pages 141-151, July.

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