The Generalized Friendship Paradox for Spectral Centralities
Social and Information Networks
2026-01-09 v2 Probability
Abstract
We revisit the classical friendship paradox which states that on an average ones friends have at least as many friends as oneself and generalize it to a variety of network centrality indices. For a broad class of spectral centralities on connected undirected graphs degree, eigenvector centrality, walk counts, Katz centrality and PageRank, we show that the average centrality of a nodes neighbours always exceeds the global average centrality.
Keywords
Cite
@article{arxiv.2507.13059,
title = {The Generalized Friendship Paradox for Spectral Centralities},
author = {Rajat Subhra Hazra and Evgeny Verbitskiy},
journal= {arXiv preprint arXiv:2507.13059},
year = {2026}
}
Comments
12 pages. Title changed. Typos corrected. To appear in Journal of Complex Networks