度-度相关下PageRank的行为
PageRank's behavior under degree-degree correlations
摘要：
本文的工作重点是在大型无标度有向网络上对Google的PageRank算法的尾部分布进行渐近分析。特别是，主要定理提供的收敛性，在Kantorovich-Rubinstein度量，随机选择的顶点在图形中产生的通过一个有向配置模型或非齐次随机有向图的秩。该定理通过将极限分布表示为i.i.d.~分支分布不动点方程的吸引内生解的副本。此外，我们提供了极限的渐近尾部行为，并用它来解释底层图中的入度/出度相关性对PageRank定性性能的影响。
英文摘要：
The focus of this work is the asymptotic analysis of the tail distribution of Google's PageRank algorithm on large scale-free directed networks. In particular, the main theorem provides the convergence, in the Kantorovich-Rubinstein metric, of the rank of a randomly chosen vertex in graphs generated via either a directed configuration model or an inhomogeneous random digraph. The theorem fully characterizes the limiting distribution by expressing it as a random sum of i.i.d.~copies of the attracting endogenous solution to a branching distributional fixed-point equation. In addition, we provide the asymptotic tail behavior of the limit and use it to explain the effect that in-degree/out-degree correlations in the underlying graph can have on the qualitative performance of PageRank.
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。
