Measuring the Generalized Friendship Paradox in Networks with Quality-dependent Connectivity

TL;DR

This paper models the generalized friendship paradox in networks considering node qualities and degrees, revealing how quality distribution influences the paradox through analytical methods and contrasting correlated and uncorrelated networks.

Contribution

It introduces a preferential attachment model incorporating node qualities, providing analytical measures of the generalized friendship paradox and comparing effects of degree-quality correlations.

Findings

Quality distribution significantly affects the paradox.

Mean and median measures yield different insights.

Correlated networks exhibit stronger paradox effects.

Abstract

The friendship paradox is a sociological phenomenon stating that most people have fewer friends than their friends do. The generalized friendship paradox refers to the same observation for attributes other than degree, and it has been observed in Twitter and scientific collaboration networks. This paper takes an analytical approach to model this phenomenon. We consider a preferential attachment-like network growth mechanism governed by both node degrees and `qualities'. We introduce measures to quantify paradoxes, and contrast the results obtained in our model to those obtained for an uncorrelated network, where the degrees and qualities of adjacent nodes are uncorrelated. We shed light on the effect of the distribution of node qualities on the friendship paradox. We consider both the mean and the median to measure paradoxes, and compare the results obtained by using these two statistics.