Scientists Prove There Are Just Six Degrees of Separation in a Social Network

A simple pattern links billions of people: just a few connections apart. New research suggests this may be an unavoidable feature of human networks.

Most people have experienced it. You mention a name, and someone responds, “I know someone who knows them.” Somehow, even in a world of billions, people are often linked by just a handful of connections. For decades, this idea has been summed up as “six degrees of separation.” Now, researchers say this pattern is not just a social curiosity. It may be an unavoidable outcome of how humans build relationships.

The concept became famous in 1967, when Harvard psychologist Stanley Milgram launched a simple but clever experiment. He mailed letters to randomly selected people in the Midwest, asking them to get the message to a specific individual in Boston. The catch was that they could only pass the letter to someone they knew personally, ideally someone who might be closer to the target.

Not every letter reached its destination. In fact, most did not. But the ones that did revealed something striking. On average, it took only about six steps, or “handshakes,” to connect the sender and recipient. This result gave rise to the idea that we live in a “small world” separated by roughly six degrees.

Evidence from Modern Networks

Although Milgram’s study had limitations, including the many letters that never arrived, later research supported the finding. Studies of Facebook users show that people are typically five to six connections apart. Similar patterns appear in email networks, actor collaborations, scientific partnerships, and even messaging platforms like Microsoft Messenger. Across very different systems, the same short distances keep appearing.

Why does this happen? A study published in Physical Review X, involving researchers from Israel, Spain, Italy, Russia, Slovenia, and Chile, offers an explanation based on how people build relationships.

In any social network, individuals aim to improve their position. It is not just about having many connections, but about forming the right ones that place them at important points within the network. For example, being connected to people who link different groups can increase access to information and influence.

But connections come with a cost. Maintaining friendships takes time and effort. Because of this, people constantly adjust their social ties, forming new ones while letting others fade. This ongoing balancing act shapes the structure of the entire network.

A Mathematical Explanation

According to the researchers, this process eventually settles into a stable pattern. Each person reaches a position that balances their desire for influence with the limits of maintaining relationships. Remarkably, when the team modeled this behavior mathematically, the result consistently produced networks where the average separation between individuals is about six steps.

“When we did the math,” says Prof. Baruch Barzel, one of the paper’s lead authors, “We discovered an amazing result: this process always ends with social paths centered around the number six. This is quite surprising. We need to understand that each individual in the network acts independently, without any knowledge or intention about the network as a whole. But still, this self-driven game shapes the structure of the entire network. It leads to the small world phenomenon, and to the recurring pattern of six degrees.”

These short paths are more than an interesting observation. They play a central role in how networks function. The rapid spread of information, trends, and ideas depends on the fact that people are only a few steps apart.

The same structure also allows diseases to travel quickly. The COVID pandemic highlighted how fast infections can move through global networks. In just a handful of transmission steps, a virus can reach distant parts of the world.

At the same time, this interconnectedness can have positive effects. As Prof. Barzel notes, “This collaboration is a great example of how six degrees can play in our favor. How else would a team from six countries around the world come together? This is truly six degrees in action!”

Reference: “Why Are There Six Degrees of Separation in a Social Network?” by I. Samoylenko, D. Aleja, E. Primo, K. Alfaro-Bittner, E. Vasilyeva, K. Kovalenko, D. Musatov, A. M. Raigorodskii, R. Criado, M. Romance, D. Papo, M. Perc, B. Barzel and S. Boccaletti, 31 May 2023, Physical Review X.

DOI: 10.1103/PhysRevX.13.021032

This study was supported by grants from the Israel Science Foundation (Grant No. 499/19), the Israel-China ISF-NSFC joint research program, and the Bar-Ilan University Data Science Institute.

Never miss a breakthrough: Join the SciTechDaily newsletter.
Follow us on Google and Google News.