Quantifying the Strength of the Friendship Paradox

The friendship paradox is the observation that friends of individuals tend to have more friends or be more popular than the individuals themselves. In this work, we first develop local metrics that quantify the strength and the direction of the paradox from the perspective of individual nodes, i.e., is the individual more or less popular than its friends. We aggregate the local measures to define global metrics that capture the friendship paradox at the network scale. Theoretical results are shown that support the global metrics to be well-behaved enough to capture the friendship paradox. Furthermore, through experiments, we identify regimes in network models, and real networks, where the friendship paradox is prominent. By conducting a correlation study between the proposed metrics and assortativity, we experimentally demonstrate that the phenomenon of the friendship paradox is related to the well-known phenomenon of homophily or assortative mixing.