On average it seems to be that we have fewer friends than most of our friends have – but can this be true for everyone? Steven Strogatz, in an article in the New York Times, claims that it is indeed the case:
Don’t believe it? Consider these results from a colossal recent study of Facebook by Johan Ugander, Brian Karrer, Lars Backstrom and Cameron Marlow. They examined all of Facebook’s active users, which at the time included 721 million people — about 10 percent of the world’s population — with 69 billion friendships among them. First, the researchers looked at how users stacked up against their circle of friends. They found that a user’s friend count was less than the average friend count of his or her friends, 93 percent of the time. Next, they measured averages across Facebook as a whole, and found that users had an average of 190 friends, while their friends averaged 635 friends of their own.
Studies of offline social networks show the same trend. It has nothing to do with personalities; it follows from basic arithmetic. For any network where some people have more friends than others, it’s a theorem that the average number of friends of friends is always greater than the average number of friends of individuals.
This phenomenon has been called the friendship paradox. Its explanation hinges on a numerical pattern — a particular kind of “weighted average” — that comes up in many other situations. Understanding that pattern will help you feel better about some of life’s little annoyances.
Most of the work done on this phenomenon stems from a classic paper published in 1991 by Scott L. Feld called (unsurprisingly) “Why your friends have more friends than you do” [American Journal of Sociology, Vol. 96, No. 6 (May 1991), pp. 1464–1477], you can click on this link: American_Journal_of_Sociology_1991_Feld to access the full paper.