增长中社交网络对齐夫定律的预测和验证
Predicted and Verified Deviation from Zipf's Law in Growing Social Networks
摘要：
齐普夫幂律是在许多自然和社会系统中发现的普遍经验规律。最近发展的一个理论预测，齐普夫定律对应于在随机比例增长、随机出生和死亡过程存在的情况下，根据最大可持续路径增长的系统。我们报告了一个新兴的社会群体网络，其中所需的Zipf定律适用的所有成分是可验证和验证的详细的实证分析。我们估计经验的平均增长$r$和它的标准差$σ$以及死亡率$h$和预测没有可调参数的指数$μ$的幂律分布$P(s)$的组大小$s$。预测值$μ= 0.75 \pm 0.05$与极大似然估计非常一致。根据理论，$P(s)$与齐普夫定律的偏差（即，$μ< 1$）构成了社会领域整体非平稳增长的直接统计定量特征。
英文摘要：
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 $σ$ 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 $s$. The predicted value $μ= 0.75 \pm 0.05$ is in excellent agreement with maximum likelihood estimations. According to theory, the deviation of $P(s)$ from Zipf's law (i.e., $μ< 1$) constitutes a direct statistical quantitative signature of the overall non-stationary growth of the social universe.
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