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Friday June 02, 2023 at 06:30

Mathematics explains the phenomenon of six degrees of separation

Recently, a group of researchers from around the world discovered that this intriguing phenomenon is linked to another social experience that we all know very well: the cost-benefit relationship in establishing new social ties.

Writing / Irene Vega

Do you know someone who knows someone? We've all played this game, often to be surprised that despite the vast scope of human society, people can be linked randomly through very small chains of acquaintances. Usually made of around six contacts.

A study, recently published in the prestigious scientific journal Physical Review (published by the American Physical Society) shows that simple human behavior can uncover the roots of this curious phenomenon. Weighing the costs and benefits of social ties, the scientific team has observed that social networks tend to have extremely short paths and, most importantly, seem to universally favor the magic number of six. But why?.

The starting point of this research begins by considering that an individual wants to gain prominence in a social network, browsing that network and looking for strategic ties. “The game is not just chasing a lot of connections, but getting the right connections. In other words, those that place the individual in a central position in the network”, explains Stefano Boccaletti, a URJC researcher and co-author of the study. “For example, looking for a junction that serves as a bridge between many roads and, therefore, channels a large part of the flow of information on the network. Of course, such network centricity, while offering extremely valuable social capital, does not come for free. Friendship has a cost. It requires constant maintenance,” he adds. 

As a result, research shows that social networks, whether offline (offline) or in the virtual environment (online), are a dynamic hive of people constantly playing the cost-benefit game, cutting connections on the one hand, and establishing new ones on the other.

“When we did the calculations,” explains Stefano Boccaletti, “we discovered an amazing result: that this process always ends with social paths around the number six. This is pretty amazing. It must be understood that everyone in the network acts independently, on their own, without considering the network as a whole. But even so, this autonomous game shapes the structure of the entire network. It leads to the small world phenomenon and the recurring pattern of six degrees of separation. This allows one to appreciate the power and beauty of network science and how it surrounds us, as well as to understand and value, at the same time, the intimate link between what we sometimes (wrongly) think of as just abstract mathematical analysis and what It is a seemingly simple phenomenon that happens every day around us.”

The shortcuts that characterize social networks are not merely a curiosity. They are a defining characteristic of network behavior. Our ability to spread information, ideas, and trends that sweep across society is deeply rooted in the fact that it only takes a few hops to link seemingly unrelated individuals.

But this phenomenon is not only applicable to ideas or messages that are spread through social connections. Viruses and other pathogens also use them. During the COVID-19 pandemic, the serious consequences of this social connection with its rapid spread were confirmed. "In fact, within six cycles of infection, a virus can cross the world," says Stefano Boccaletti.

On the plus side though, this research is a great example of how the six degrees can be helpful too. This study, partially funded by the Rey Juan Carlos University, has brought together scientists from Italy, Israel, Slovenia, Russia, South America and Spain. This research team is led by Stefano Boccaletti and includes other URJC members: Regino Criado and Miguel Romance, university professors, and young researchers such as David Aleja, Eva Primo and Karin Alfaro-Bittner. In addition, they are part of the mathematical team of the Moscow Institute of Physics and Technology, Israeli and Italian statistical physicists, as well as Slovenian experts.

Milgram's experiment

In 1967, a farmer in Omaha, Nebraska, USA, received a peculiar letter in his mailbox. The sender was Professor Stanley Milgram of Harvard University, and the recipient was his X friend, a Boston stockbroker. "In case you know X," the message read, "please send him this letter."

Of course, the chances of having such a direct acquaintance across social and geographic distance—from Omaha to Boston in the 60s—were extremely slim. And therefore the letter also requested that if the recipient did not know X directly, he should forward the letter to someone who could.

This letter was one of approximately 1.000 identical packages sent with similar instructions. So these 1.000 independent charters began circulating across the US in search of a social path linking the Central American farmer with the East Coast X broker.

As a result of this experiment by Professor Milgram, not all chains closed, but those that did, experimentally recorded, for the first time, the social pathways that connect American society. The paths were found to be extremely short.

 “In a society of hundreds of millions of people, according to the experiment, only about six handshakes were needed to establish a bridge between two random people”, explain Regino Criado and Miguel Romance. "In fact, the Milgram experiment confirmed what many of us intuit: that we live in a small world, divided by only six degrees of separation."

However, this innovative experiment was also considered unreliable due to being skewed by how few cards actually succeeded. Although his findings have been subsequently reaffirmed in a series of more systematic studies. For example, the millions of Facebook users are separated on average by 5-6 clicks. Similar distances have also been measured in 24.000 email users, stakeholder networks, scientific collaboration networks, the Microsoft Messenger network, and many others.

In short, it has been observed that the six degrees of separation are in all areas and social connections.