互联网波动中的交叉跃迁
Crossover transition in the Fluctuation of Internet
摘要：
Gibrat定律预测节点度增长率的标准差是常数。另一方面，优先附着（PA）表明，这样的标准偏差随着初始程度的指数$-0.5$的幂律减少。虽然这两种模型都已应用于互联网建模，但这种不一致性需要验证其有效性。因此，我们实证研究了三个不同的时间间隔（日，月和年）的互联网波动。我们发现了一个从PA模型到Gibrat定律的交叉过渡，这是从未报道过的。具体地说，周期律从小度区域开始，随着观测周期的增加逐渐扩展。我们确定了两个模型的有效期，发现内部联系之间的相关性对Gibrat定律的出现有很大的贡献。这些发现表明PA和Gibrat定律都不适用于实际的互联网，这需要一个更完整的模型理论。
英文摘要：
Gibrat's law predicts that the standard deviation of the growth rate of a node's degree is constant. On the other hand, the preferential attachment(PA) indicates that such standard deviation decreases with initial degree as a power law of exponent $-0.5$. While both models have been applied to Internet modeling, this inconsistency requires the verification of their validation. Therefore we empirically study the fluctuation of Internet of three different time intervals(daily, monthly and yearly). We find a crossover transition from PA model to Gibrat's law, which has never been reported. Specifically Gibrat-law starts from small degree region and extends gradually with the increase of the observed period. We determine the validated periods for both models and find that the correlation between internal links has large contribution to the emergence of Gibrat law. These findings indicate neither PA nor Gibrat law is applicable to the actual Internet, which requires a more complete model theory.
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