PageRank双对数图背后的决定因素
Determining factors behind the PageRank log-log plot
摘要：
研究了PageRank与信息网络的入度、出度、悬空节点数等参数之间的关系。我们通过一个受PageRank原始定义启发的随机方程来建模这种关系。此外，我们使用规则变化的理论证明，PageRank和入度遵循幂律具有相同的指数。这两个幂律之间的差异是在一个倍数系数，这主要取决于悬挂节点的分数，平均度，幂律指数，和阻尼因子。出度分布有一个较小的影响，我们明确量化。我们的理论预测显示出良好的协议与实验数据上的三个不同的样本的Web。
英文摘要：
We study the relation between PageRank and other parameters of information networks such as in-degree, out-degree, and the fraction of dangling nodes. We model this relation through a stochastic equation inspired by the original definition of PageRank. Further, we use the theory of regular variation to prove that PageRank and in-degree follow power laws with the same exponent. The difference between these two power laws is in a multiple coefficient, which depends mainly on the fraction of dangling nodes, average in-degree, the power law exponent, and damping factor. The out-degree distribution has a minor effect, which we explicitly quantify. Our theoretical predictions show a good agreement with experimental data on three different samples of the Web.
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