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Empirical test of the origin of Zipf’s law in growing social networks

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  • Zhang, Qunzhi
  • Sornette, Didier

Abstract

Zipf’s power law is a general empirical regularity found in many systems. We report a detailed analysis of a burgeoning network of social groups, in which all ingredients needed for Zipf’s law to apply are verifiable and verified. A recently developed theory predicts that Zipf’s law corresponds to systems that are growing according to a maximally sustainable path in the presence of random proportional growth, stochastic birth and death processes. We estimate empirically the average growth r and its standard deviation σ as well as the death rate h and predict without adjustable parameters the exponent μ of the power law distribution P(s) of the group sizes s. Using numerical simulations of the underlying growth model, we demonstrate that the empirical stability of Zipf’s law over the whole lifetime of the social network can be attributed to the interplay between a finite lifetime effect and a large σ value. Our analysis and the corresponding results demonstrate that Zipf’s law can be observed with a good precision even when the balanced growth condition is not realized, if the random proportional growth has a strong stochastic component and is acting on young systems under development.

Suggested Citation

  • Zhang, Qunzhi & Sornette, Didier, 2011. "Empirical test of the origin of Zipf’s law in growing social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4124-4130.
  • Handle: RePEc:eee:phsmap:v:390:y:2011:i:23:p:4124-4130
    DOI: 10.1016/j.physa.2011.06.063
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    Citations

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    Cited by:

    1. Zhu, Zhiguo, 2013. "Discovering the influential users oriented to viral marketing based on online social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(16), pages 3459-3469.
    2. Didier Sornette & Thomas Maillart & Giacomo Ghezzi, 2014. "How Much Is the Whole Really More than the Sum of Its Parts? 1 ⊞ 1 = 2.5: Superlinear Productivity in Collective Group Actions," PLOS ONE, Public Library of Science, vol. 9(8), pages 1-15, August.
    3. Malevergne, Y. & Saichev, A. & Sornette, D., 2013. "Zipf's law and maximum sustainable growth," Journal of Economic Dynamics and Control, Elsevier, vol. 37(6), pages 1195-1212.
    4. Li, Jun-fang & Zhang, Bu-han & Liu, Yi-fang & Wang, Kui & Wu, Xiao-shan, 2012. "Spatial evolution character of multi-objective evolutionary algorithm based on self-organized criticality theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5490-5499.
    5. Didier Sornette & Spencer Wheatley & Peter Cauwels, 2019. "The Fair Reward Problem: The Illusion Of Success And How To Solve It," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-52, May.

    More about this item

    Keywords

    Zipf’s law; Gibrat’s law;

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