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arXiv · 2507.13059

The Generalized Friendship Paradox for Spectral Centralities

Rajat Subhra Hazra·Evgeny Verbitskiy
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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.

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Rajat Subhra Hazra, Evgeny Verbitskiy. 2026-01-08. The Generalized Friendship Paradox for Spectral Centralities. https://arxiv.org/abs/2507.13059

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