网页的度内和PageRank：为什么它们遵循相似的幂律？
In-Degree and PageRank of Web pages: Why do they follow similar power laws?
摘要：
PageRank是Google设计的一种流行度衡量标准，用于对网页进行排名。实验证实，PageRank服从“幂律”，其指数与In度相同。本文提出了一种新的数学模型来解释这一现象。PageRank和入度之间的关系通过一个随机方程来建模，该随机方程的灵感来自PageRank的原始定义，并且类似于M/G/1队列中忙期的著名分布恒等式。此外，我们采用正则变分理论和Tauberian定理来分析证明PageRank和In度的尾部行为仅相差一个乘法因子，为此我们导出了一个封闭形式的表达式。我们的分析结果与实验数据吻合得很好。
英文摘要：
The PageRank is a popularity measure designed by Google to rank Web pages. Experiments confirm that the PageRank obeys a `power law' with the same exponent as the In-Degree. This paper presents a novel mathematical model that explains this phenomenon. The relation between the PageRank and In-Degree is modelled through a stochastic equation, which is inspired by the original definition of the PageRank, and is analogous to the well-known distributional identity for the busy period in the M/G/1 queue. Further, we employ the theory of regular variation and Tauberian theorems to analytically prove that the tail behavior of the PageRank and the In-Degree differ only by a multiplicative factor, for which we derive a closed-form expression. Our analytical results are in good agreement with experimental data.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
