Physical Sciences and Mathematics Commons^™

A Study On The Friendship Paradox – Quantitative Analysis And Relationship With Assortative Mixing, Siddharth Pal, Feng Yu, Yitzchak Novick, Ananthram Swami, Amotz Bar-Noy

Lander College of Arts and Sciences Publications and Research

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 study local metrics to capture the strength of the paradox and the direction of the paradox from the perspective of individual nodes, i.e., an indication of whether the individual is more or less popular than its friends. These local metrics are aggregated, and global metrics are proposed to express the phenomenon on a network-wide level. Theoretical results show that the defined metrics are well-behaved enough to capture the friendship paradox. We also …