In a world of billions of people, are there really only about six people between you and any stranger? An international research team led by Israel's Bar-Ilan University recently published a study in "Physical Review
The concept of “six degrees of separation” originated in the 1960s. In 1967, Harvard psychologist Stanley Milgram designed a famous experiment: He mailed letters to random subjects in the Midwestern United States, asking them to try to deliver the letter to a specific target person in Boston on the premise that it would only be delivered through "people they knew." While most of the letters never arrived, those that did showed that they only passed an average of about six times between sender and recipient, a result that gave rise to the saying that "we live in a small world."
Since then, with the development of the Internet and social media, more and more large-scale data have provided support for this phenomenon. Research has found that on social platforms such as Facebook, there are only five to six "friend relationships" between any two users on average; similar "short path" structures also appear in email exchange networks, film and television actor collaboration networks, scientist co-authorship networks, and instant messaging platforms. No matter how different the systems are, the pattern of "connecting in a few steps" keeps recurring.
The key question the new study attempts to answer is: Why does this result occur? Researchers from Israel, Spain, Italy, Russia, Slovenia, Chile and other countries have proposed that a person's social connections are not just about "more", but also about "good location" - for example, establishing connections with "bridge figures" who connect different groups, which helps to obtain information and influence. However, maintaining each relationship requires time and energy. In real life, people have to constantly make trade-offs and dynamically adjust between establishing new relationships and giving up old relationships. This continuous game shapes the structure of the entire social network.
On this basis, the research team established a mathematical model to simulate the process of individuals pursuing more favorable network positions under limited resource constraints. They found that when this process evolves over a period of time, it will tend to a stable state: everyone is at a balance point between "influence benefits" and "relationship maintenance costs." Surprisingly, no matter how the parameters are adjusted, this self-organizing process ultimately generates a "small world" network in which the average distance between any two people naturally converges to about six steps.
Professor Baruch Bazell, one of the authors of the paper, pointed out that the reason why this result is "astonishing" is that each individual in the model only makes local decisions based on its own situation, does not understand the entire network structure, and does not deliberately pursue the goal of "six degrees of separation." But at the macro level, millions of such local choices jointly shape a stable small world structure, thereby "automatically" producing a social distance of about six steps.
The research emphasizes that this short-path structure is not only an interesting statistical phenomenon, but also profoundly affects the way the real world operates. An important prerequisite for the rapid spread of information, opinions and popular culture on a global scale is that people are only a few steps away from each other on the Internet. The same mechanism also explains the rapid spread of infectious diseases: as the COVID-19 pandemic has shown, viruses can span vast geographical and social distances after just a few rounds of transmission.
However, tightly connected networks also create the conditions for collaboration. Professor Barzel pointed out that this study itself is an example of "six degrees of separation" - scientists from six countries can form a joint team precisely because researchers from different regions and different fields can ultimately be connected 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?", co-signed by I. Samoylenko, D. Aleja, B. Barzel and others, and funded by the Israel Science Foundation, the Israel-China Joint Research Project, and the Bar-Ilan University Data Science Institute. The research team believes that providing a universal mathematical explanation for "six degrees of separation" will not only deepen people's understanding of the structure of social networks, but also help make more targeted decisions in the fields of public health, information dissemination, and network governance.