The friendship paradox is the observation that the degrees of a node’s neighbors within a network will, on average, be greater than the degree of the node itself. In other words: your friends probably have more friends than you.
While the standard framework of the Friendship Paradox is primarily about averages, there are significant variations as well.
In the Complex Networks Journal, researchers from the Santa Fe Institute and the University of Michigan, George Cantwell, Alec Kirkley and Mark Newman, tackle this problem by developing the mathematical theory of the friendship paradox.
Some people have a lot of friends, while others only have a few. Unless you have good reason to believe otherwise, it’s safe to assume that you have roughly an average number of friends.
But if you compare yourself to your friends, you may see a different picture. In fact, a simple calculation – provided by Scott L. Field’s 1991 article “Why Your Friends Have More Friends Than You” – shows that it is likely that many of your friends are more popular than you.
Almost by definition, your friends are likely to be the kind of people who have a lot of friends. Perhaps worse, this effect means that your friends might not only be more popular than you, but also wealthier and more attractive.
These types of friendship paradoxes have been explored by network scientists for 30 years.
“Standard analyzes are about average behavior, but there is a lot of heterogeneity among people,” Cantwell explains. “Could the average results, for example, be skewed by a few outliers? To get a more complete picture, we looked at the full distribution of how people compare to their friends – not just the average.”
The researchers found that applying math to real-world data reveals a slightly more nuanced picture. For example, popular people are more likely to be friends with each other, while less popular people are more likely to be friends with less popular people.
Conversely, some people have only one or two friends, while others have hundreds. “It tends to amplify the effect,” Cantwell explains. “While there are surely other effects at play, about 95% of the variation within social networks can be explained by these two alone.”
We should all “just be wary of the impressions we get about our success and our social status by looking at the people around us, because we have a distorted view,” Cantwell adds. “In the offline social world, the bias is partially mitigated by the fact that we tend to hang out around other like-minded people. In online social networks, however, the effect can be exacerbated – there is has virtually no limit on the number of people who can follow someone online, and no reason to only watch “like” people.
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Material provided by Santa Fe Institute. Note: Content can be changed for style and length.