Influence of the automorphism group of a graph on its PageRank scores of vertices

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2025-04-22 DOI:10.1016/j.aam.2025.102900

Dein Wong , Qi Zhou , Xinlei Wang

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引用次数: 0

Abstract

Google's success derives in large part from its PageRank algorithm, which assign a score to every web page according to its importance. Recently, G. Modjtaba et al. (2021) [19] proved that similar vertices in a graph have the same PageRank score and they proposed a conjecture, suspecting that two graphs are completely non-Co-PR if they are non-Co-PR graphs. The investigation of this paper mainly concerns the influence of the automorphism group of a graph on its PageRank scores of vertices. The main results of this article are as follows.

1.
Based on matrix analysis, two conditions on what kinds of vertices have the same PageRank score are obtained.
2.
Four techniques for constructing Co-PR graphs are established.
3.
A non-regular connected graph of order n, with $\frac{1}{n}$ as PR scores of most of its vertices, is constructed, which provides a negative answer to Modjtaba's conjecture above.

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图的自同构群对顶点PageRank分数的影响

b谷歌的成功在很大程度上得益于其PageRank算法，该算法根据每个网页的重要性给其打分。最近，G. Modjtaba等人（2021）[19]证明了图中相似的顶点具有相同的PageRank得分，并提出了一个猜想，如果两个图是非co - pr图，则怀疑它们是完全非co - pr图。本文主要研究图的自同构群对其顶点PageRank分数的影响。本文的主要研究结果如下：基于矩阵分析，得到了哪种顶点具有相同PageRank分数的两个条件。建立了四种构建Co-PR图的技术。构造了一个n阶的非正则连通图，其中大部分顶点的PR值为1n，给出了上述Modjtaba猜想的否定答案。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Applied Mathematics 数学-应用数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

85 days

期刊介绍： Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas. Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.