Quantifying the Strength of the Friendship Paradox

Abstract

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.

Research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-09-2-0053 (the ARL Network Science CTA). The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation here on. This document does not contain technology or technical data controlled under either the U.S. International Traffic in Arms Regulations or the U.S. Export Administration Regulations.