RAMAT-GAN, Israel — Kevin Bacon, this study is for you! In an exciting breakthrough, researchers from multiple countries have unraveled the mystery behind the “six degrees of separation” phenomenon. You know that game where you try to connect people through acquaintances? It turns out, on average, it really does only take about six handshakes to link any two random individuals in our vast human society. Now, scientists have mathematically can explain why this magic number exists.
Back in 1967, Professor Stanley Milgram from Harvard University conducted a fascinating experiment. He sent around 300 identical packages across the United States with instructions to pass the letter within social circles to eventually reach the intended recipient. Through this experiment, he discovered that social paths connecting people were astonishingly short, typically just six handshakes away.
Since then, similar studies on various social networks, including Facebook, email users, actor networks, and scientific collaboration networks, have consistently shown that the average number of handshakes to link any two people is six. But what drives this pattern?
A recent paper published in Physical Review X by researchers from Israel, Spain, Italy, Russia, Slovenia, and Chile sheds light on the mechanism behind this phenomenon. It all comes down to human behavior and the constant balance between the costs and benefits of establishing new social ties.
People naturally seek prominence in social networks, strategically choosing connections that place them in central positions. However, forging new friendships requires effort and maintenance, which comes with a cost. So, individuals in social networks constantly play the cost-benefit game, breaking old ties and forming new ones to achieve an equilibrium that balances their desire for prominence and their limited social budget.
“When we did the math, we discovered an amazing result: this process always ends with social paths centered around the number six. Each individual acts independently without knowing the network as a whole, yet this self-driven game shapes the structure of the entire network, leading to the small world phenomenon and the recurring pattern of six degrees,” lead author Baruch Barzel, a professor at Bar-Ilan University, explains in a statement.
Breaking down cost and benefit of social connections
The study focused on a network of nodes—each representing a “rational agent” or individual—interacting within a game. These agents can decide to form connections or “links” with others based on two factors — as mentioned, cost and benefit. The “cost” aspect is straightforward. Maintaining a connection with another individual incurs a cost, which may be constant or could vary depending on the size of the network. On the flip side, the “benefit” is measured in terms of an agent’s influence within the network, calculated by a metric called “betweenness centrality.”
Betweenness centrality essentially gauges how essential a node (or person) is in facilitating connections between other nodes. Imagine you’re friends with both a filmmaker and a film critic; you’re central in the connection between these two people. The study adds an innovative twist to this measure by considering the “length” of the path through which an individual connects others, thereby giving a weighted importance to more direct connections.
‘Within this game, every agent continually evaluates whether forming new connections will improve their network influence or if maintaining existing connections is more beneficial. They make these decisions based on a balance between the associated costs and the projected benefits, aiming to maximize their influence within the network.
Six Degrees Of Separation — For Just About Anything
When the game reaches a point where no individual has anything to gain by changing their existing connections—a situation known as Nash equilibrium—the resulting network naturally exhibits the characteristic of six degrees of separation. This means that any two people in the network could be connected through six or fewer intermediaries, offering a solid explanation for the phenomenon that has intrigued social scientists and the general public alike.
Understanding the underlying mechanics of networks, especially the six degrees of separation concept, has broad implications. It can help in designing more efficient social platforms, optimizing transportation systems, or even predicting the spread of diseases. As witnessed during the rapid spread of the COVID pandemic, within six infection cycles, a virus can span the globe. With this research, scientists have not just explained a longstanding societal observation but have also provided tools for practical applications in various domains.
The findings provide a fascinating glimpse into the intricacies of human social networks and the underlying mathematics that shape our small world, after all. On a positive note, this study is also a testament to the power of six degrees in bringing together a diverse team of researchers from six different countries. The collaboration showcases how interconnected our world has become, thanks to the magic of six degrees.
The study was supported by grants from the Israel Science Foundation, the Israel-China ISF-NSFC joint research program, and the Bar-Ilan University Data Science Institute.