PAGERANK ASYMPTOTICS ON DIRECTED PREFERENTIAL ATTACHMENT NETWORKS

• 成果类型: Article
• 署名作者: Banerjee, Sayan; Olvera-Cravioto, Mariana
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1757
• 发表日期: 2022
• 页码: 3060-3084
• 关键词: convergence; BEHAVIOR; trees; web

摘要

We characterize the tail behavior of the distribution of the PageRank of a uniformly chosen vertex in a directed preferential attachment graph and show that it decays as a power law with an explicit exponent that is described in terms of the model parameters. Interestingly, this power law is heavier than the tail of the limiting in-degree distribution, which goes against the commonly accepted power law hypothesis. This deviation from the power law hypothesis points at the structural differences between the inbound neighborhoods of typical vertices in a preferential attachment graph versus those in static random graph models where the power law hypothesis has been proven to hold (e.g., directed configuration models and inhomogeneous random digraphs). In addition to characterizing the PageRank distribution of a typical vertex, we also characterize the explicit growth rate of the PageRank of the oldest vertex as the network size grows.