Mathematical Theory of The Friendship Paradox


The friendship paradox is the empirical observation made by sociologist Scott Feld in 1991 while studying the properties of social networks to calculate the average number of friends that a person in the network has and compared this to the average number of friends that these friends had discovered that your friends have more friends than you do.

Recently in the Journal of Complex Networks, Santa Fe Institute and University of Michigan researchers George Cantwell, Alec Kirkley, and Mark Newman address this observation by developing the mathematical theory of the friendship paradox.


Generally, the paradox arises because number of friends people have been distributed in a way that follows a power law rather than an ordinary linear relationship so most people have a few friends while a small number of people have lots of friends.

‘Popular people are more likely to be friends with one another, whereas less popular people are more likely to be friends with less popular people.’


We should all “simply be wary of impressions we get about our success and social status from looking at the people around us because we get a distorted view”, says Cantwell, key researcher.

The researchers claim that applying mathematics to real-world data reveals a slightly more variation in the paradox and need to study the full distribution of describing how people compare to their all friends not just the average friends can reduce the significant implications for the way people perceive themselves given that their friends will always seem happier, wealthier and more popular than they are.

Source: Medindia



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