Mathematics Application Takes ‘Friendship Paradox” Beyond Average

Science News – In network science, the famous ‘friendship paradox’ describes why your friends are (on average) more popular, richer, and more attractive than you are. But a slightly more nuanced picture emerges when researchers apply mathematics to real-world data.

In a new study published in the Journal of Complex Networks, researchers at the Santa Fe Institute and the University of Michigan developed a revolutionary mathematical theory of the friendship paradox. Scott L. Field’s 1991 paper included a simple calculation that showed that it’s likely many of your friends are more popular than you.

The researchers suggested that though the standard framing of the friendship paradox is about averages, significant differences also can occur. They applied mathematics to real-world data and found a more nuanced picture. For example, more popular individuals tend to be friends with more popular ones, while the less popular individuals are more likely to be friends with the less popular ones.

“Standard analyses are concerned with average behavior, but there’s a lot of heterogeneity among people,” said George Cantwell, researcher of the University of Michigan.

Contrarily, some people have one or two friends and others have hundreds. “This has a tendency to magnify the effect. While there are surely other effects at play, around 95% of the variation within social networks can be explained by just these two,” Cantwell added further.

According to him, people should be wary of impressions that they get about their success and social status from looking at others around them because they get a distorted view.

“In the offline social world, the bias is partially mitigated by the fact we tend to end up around similar others. On online social media, however, the effect can be exacerbated — there’s virtually no limit on the number of people who can follow someone online and no reason to only look at ‘similar’ people,” Cantwell explained.

To Know More You May Refer To:

Cantwell, G. T., Kirkley, A., & Newman, M. E. (2021). The friendship paradox in real and model networks. Journal of Complex Networks, 9(2). https://doi.org/10.1093/comnet/cnab011