Predicted and Verified Deviation from Zipf's Law in Growing Social Networks

Details Predicted and Verified Deviation from Zipf's Law in Growing Social Networks Predicted and Verified Deviation from Zipf's Law in Growing Social Networks

2010-07-15

arxiv.org/abs/1007.2650v1

Physics

Physics and Society

4 pages, 2 figures, 2 tables

Scientific paper

Zipf's power law is a general empirical regularity found in many natural and social systems. 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 report a detailed empirical analysis of a burgeoning network of social groups, in which all ingredients needed for Zipf's law to apply are verifiable and verified. We estimate empirically the average growth $r$ and its standard deviation $\sigma$ as well as the death rate $h$ and predict without adjustable parameters the exponent $\mu$ of the power law distribution $P(s)$ of the group sizes $s$. The predicted value $\mu = 0.75 \pm 0.05$ is in excellent agreement with maximum likelihood estimations. According to theory, the deviation of $P(s)$ from Zipf's law (i.e., $\mu < 1$) constitutes a direct statistical quantitative signature of the overall non-stationary growth of the social universe.

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