Generalized friendship paradox in networks with tunable degree-attribute correlation

TL;DR

This paper investigates the generalized friendship paradox in complex networks, analyzing how degree-attribute correlations influence the paradox at both network and individual levels through models and simulations.

Contribution

It introduces a model to analyze the paradox at the node level and explores the effects of degree-attribute correlations in assortative and dissortative networks.

Findings

Degree-attribute correlation affects individual paradox probability.

Assortative and dissortative networks show different relevance of correlations.

A solvable model characterizes the paradox in uncorrelated networks.

Abstract

One of interesting phenomena due to topological heterogeneities in complex networks is the friendship paradox: Your friends have on average more friends than you do. Recently, this paradox has been generalized for arbitrary node attributes, called generalized friendship paradox (GFP). The origin of GFP at the network level has been shown to be rooted in positive correlations between degrees and attributes. However, how the GFP holds for individual nodes needs to be understood in more detail. For this, we first analyze a solvable model to characterize the paradox holding probability of nodes for the uncorrelated case. Then we numerically study the correlated model of networks with tunable degree-degree and degree-attribute correlations. In contrast to the network level, we find at the individual level that the relevance of degree-attribute correlation to the paradox holding probability may depend on whether the network is assortative or dissortative. These findings help us to understand the interplay between topological structure and node attributes in complex networks.