The Generalized Friendship Paradox for Spectral Centralities

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.