POWER LAW

Dunbar’s number doesn’t represent the average number of social connections

Covid-19 is the moment of truth for Taiwan’s corporate culture.
Covid-19 is the moment of truth for Taiwan’s corporate culture.
Image: REUTERS/Nicky Loh
We may earn a commission from links on this page.

You have probably heard of “Dunbar’s Number,” which many cite as the average number of people with whom a human can have a relationship. But this idea—that there is a typical network size—isn’t what Dunbar’s Number was meant to indicate at all.

The evolutionary psychologist Robin Dunbar studied the social connections among groups of primates in the early 1990s. Through his observations, he built a theory that the size of the groups observed must have been influenced by the size of the animals’ brains. It takes brainpower to interact with other animals, to socialize and bond with them and to remember past interactions. So, the number of those interactions that a primate can keep straight must correlate to how much brainpower the animal has. Specifically, Dunbar theorized, the brain’s neocortex must correlate to how many interactions a primate can handle. Dunbar then measured the human neocortex and estimated the upper limit of humans’ ability to maintain social relationships, concluding that they can handle around 150 contacts.

Where “Dunbar’s Number” often gets misinterpreted is in the assumption that this average network size has a normal distribution—an inverted U that indicates most people cluster to the center and a few folks are outliers. In other words, they assume that most people have around 150 people in their networks. But that’s not quite the case.

Almost 20 years after Dunbar made his estimate, in 2010, a trio of researchers led by Tyler McCormick, then a PhD student in statistics at Columbia University, attempted to estimate the average size of an individual’s network using surveys and statistical calculations in lieu of brain size.  They found that the average (mean) network size of those surveyed was 611 people. Taken by itself, this number is dramatically larger than Dunbar’s estimate. But while the mean network size was 611 contacts, the median was 472 contacts. This difference might not seem like a big deal to you or me, but to a statistician it’s a clear signal that the number of contacts in people’s networks doesn’t follow a normal distribution. Instead, network sizes may follow a power law.

A power law is a different kind of distribution. Instead of a bell curve, a power law looks like the steepest hill you have ever seen. It starts high and then drops quickly before almost leveling off near the horizontal axis. In the case of networks, it means a few people have incredibly large numbers of social relationships, but most have a much smaller number.

McCormick and his colleagues are not the only people studying the presence of power laws in networks. They are not even the first. Credit for that discovery goes to Albert-László Barabási and Réka Albert. As early as the mid-1990s, Barabási and Albert were studying networks, both person-to-person and technological networks such as the world wide web. Because they were studying webpages on the Internet in addition to personal networks, they had noticed fairly early on that many websites—nodes in the network—had very large collections of hyperlinks compared to other webpages. As the world wide web evolved, certain places became the preferred starting point for Internet users, and over time these websites were linked to much more frequently than average. To the researchers, it was fairly easy to see that the pattern didn’t follow an assumed normal distribution—instead, it followed a power law.

This led them to wonder if the same phenomenon held true for human networks. In their follow-up studies, the power law held up. A small percentage of people really were better connected than everyone else. Their later research would show that not only does the power law show a dramatic upward curve in the number of connections individuals have, but once someone moves far enough up the curve, their large number of connections yield large numbers of new connections. They called this phenomenon “preferential attachment.” Once you hit a certain critical mass, your connections take over and you can’t help but be introduced to more and more people.

The rich get richer and the well-connected get even better connected.

The power law is the explanation for why some people seem like they know everybody: some people really do know way more people than you. And the presence of those super-connectors skews the average higher than the size of your network.

While it might seem like all bad news, there is an upside. If Barabási and Albert’s research is correct, then most of us have an uphill battle to fight as we grow and nurture our personal and professional networks. But we should also note that it will get easier overtime. The people who seem to know everybody may be working less on their networks then you are, but that suggests that eventually your hard work will pay dividends too.

Don’t get discouraged, just keep working on building connections. Eventually a lot of people might start to think you know everybody too.

David Burkus is the author of Friend of a Friend and Associate Professor of Leadership and Innovation at Oral Roberts University.