Scientists Use Mathematical Model to Confirm "Six Degrees of Separation" in Social Networks
In a world with billions of people, are you really only about six people away from any stranger? A recent study published in *Physical Review X* by an international research team led by Bar-Ilan University in Israel suggests that the "six degrees of separation" is not a coincidence, but a structural result inevitably driven by the way humans build social relationships.
The concept of "six degrees of separation" originated in the 1960s. In 1967, Harvard University psychologist Stanley Milgram designed a famous experiment: he mailed letters to random subjects in the American Midwest, asking them to forward the letters to a specific target person in Boston, but only through "people they knew." Although most letters were ultimately undelivered, those that successfully arrived showed that the sender and recipient were separated by an average of about six transfers, a result that gave rise to the saying "we live in a small world."
Since then, with the development of the internet and social media, more and more large-scale data have supported this phenomenon. Studies have found that on social platforms like Facebook, any two users are separated by an average of only five to six "friend connections"; similar "short path" structures also appear in email networks, film actor collaboration networks, scientist co-authorship networks, and instant messaging platforms. Regardless of how different the systems are, the pattern of "being connected within a few steps" repeatedly appears.
The key question this new research attempts to answer is: why does this happen? Researchers from Israel, Spain, Italy, Russia, Slovenia, and Chile propose that a person's social relationships are not only about "quantity" but also about "good position" – for example, establishing connections with "bridge figures" who connect different groups, which helps to acquire information and influence. However, maintaining each relationship requires time and energy, and people in real life must constantly weigh the trade-offs, dynamically adjusting between building new relationships and abandoning old ones. This ongoing game shapes the structure of the entire social network.
Based on this, the research team established a mathematical model to simulate the process of individuals pursuing more advantageous network positions under limited resource constraints. They found that when this process evolves for a period of time, it tends to stabilize: everyone is at a balance point between "influence gains" and "relationship maintenance costs." Surprisingly, regardless of how the parameters are adjusted, this self-organizing process eventually generates a "small world" network, in which the average distance between any two people naturally converges to around six steps.
Professor Baruch Barzel, one of the paper's authors, pointed out that this result is "astonishing" because each individual in the model only makes local decisions based on their own situation, without understanding the entire network structure or deliberately pursuing the goal of "six degrees of separation." However, at the macro level, millions of such local choices collectively shape the stable small-world structure, thereby "automatically" creating a social distance of about six steps.
The study emphasizes that this short-path structure is not only an interesting statistical phenomenon, but also profoundly affects the way the real world operates. The rapid spread of information, ideas, and popular culture around the globe is largely due to the fact that people are only a few steps away from each other in the network. The same mechanism also explains the rapid spread of infectious diseases: as the COVID-19 pandemic has shown, viruses can cross vast geographical and social distances after only a few rounds of transmission.
However, a tightly connected network also creates conditions for collaboration. Professor Barzel pointed out that this research itself is an example of "six degrees of separation" – the fact that scientists from six countries were able to form a joint team is because researchers from different regions and fields can ultimately connect through a few hops in the global academic network.
The research paper is titled "Why Are There Six Degrees of Separation in a Social Network?" and is co-authored by I. Samoylenko, D. Aleja, B. Barzel, and others. It was funded by the Israel Science Foundation, the Israel-China Joint Research Program, and the Bar-Ilan University Data Science Institute, among other institutions. The research team believes that providing a mathematically universal explanation for "six degrees of separation" not only deepens people's understanding of the structure of social networks, but also helps to make more targeted decisions in areas such as public health, information dissemination, and network governance.