Closed Form Solution for a Specific Case on the Friendship Paradox

Abstract

It is a common feeling among people that their friends are more popular than they are. With social networking sites like Facebook, many people find validation that, indeed, many of their friends have more "friends" than they do. This thesis examines this phenomenon, known as the Friendship Paradox, both in general and for a specific type of network. For the specific type of network, this thesis derives closed- form solutions for the average number of friends per person and for the average number of friends that each person's friends have for a group of n people. It is shown that the average number of friends of friends is greater than the average number of friends, which explains why many people do not feel as popular as their friends. Finally, other applications of this paradox are highlighted.