特征向量的广义友谊悖论
The Generalized Friendship Paradox for Eigenvectors
浏览论文内容
中文总结 AI 辅助
研究非齐次Erdős-Rényi随机图中特征向量的广义友谊悖论，考虑图邻接矩阵及最大特征值对应特征向量元素为顶点属性，推导顶点偏差值经验分布的极限分布。
中文摘要 AI 辅助
本文研究了非齐次Erdős-Rényi随机图中特征向量的广义友谊悖论（也称为特征友谊悖论，以下简称为EFP），其边概率由连续图子生成。我们考虑图的邻接矩阵，并将其最大特征值对应的特征向量的元素作为顶点属性。文献[hazra2026generalized]表明在此设置下广义友谊悖论成立。我们研究了顶点上所得偏差值的经验分布，并根据积分算子的主特征值和相应特征函数明确推导其极限分布，该积分算子的核是基础图子。
英文摘要
In this paper, we investigate the generalized friendship paradox for eigenvectors (alternatively called the eigen friendship paradox and abbreviated hereafter as EFP) in the setting of inhomogeneous Erdős--Rényi random graphs whose edge probabilities are generated by a continuous graphon. We consider the adjacency matrix of the graph and take the entries of the eigenvector corresponding to its largest eigenvalue as the vertex attributes. It was shown in \cite{hazra2026generalized} that the generalized friendship paradox holds in this setting. We study the empirical distribution of the resulting bias values across the vertices and derive its limiting distribution explicitly in terms of the principal eigenvalue and the corresponding eigenfunction of the integral operator whose kernel is the underlying graphon.
