Mathematician Musatov and colleagues scientifically explained the “rule of six handshakes”

“Immediately there is someone who wants to cut too long chains”

Everyone has heard about the so-called “close world phenomenon” or the rule of six handshakes, according to which one person can “reach out” to any other on Earth through his acquaintances and acquaintances. But no one thought about what “forces” cause such an effect. Or maybe “six handshakes” is just a figure of speech? The rule was explained using a mathematical model by MIPT scientists and their colleagues from abroad.

The results of the work were presented recently in the journal Physycal Review X of the American Physical Society.

The theory of six handshakes was put forward in 1928 by the Hungarian writer Frigyes Karinty. It consisted in the fact that each person is indirectly familiar with any other inhabitant of the planet through a chain of mutual acquaintances. In other words, having communicated indirectly with five people, you can reach a person living at least on the other side of the globe.

This theory was confirmed in the last century by sociologists who asked 300 residents of one city to send letters to an addressee in another city through acquaintances or relatives. Not all of them reached, but each of the 60 “happy” messages passed through an average of five people. Microsoft specialists also set up an experiment, following the transmission of e-mail messages. And their theory was confirmed. The effect was also shown on data from a wide variety of online social networks.

“The phenomenon of the small world itself has been known for a long time, but there was no clear explanation of where such a structure comes from,” explains one of the authors of the work, Associate Professor of the Department of Discrete Mathematics at MIPT, Daniil Musatov, explaining the choice of the topic for research. – On the one hand, the origin of the effect seems obvious: each person has about 100 acquaintances. This means that he may already have 10 thousand acquaintances of acquaintances, at the third step – a million, and so on, up to a trillion at the sixth step.

But on the other hand, the process can slow down and begin to repeat already at the second step – for example, my friends will connect me with other acquaintances of mine, and not with new people. We decided to try to replicate the effect by creating a mathematical model.

For its objects, we took a lot of “agents” who primarily pursue their interests in the network (or in society). There are supposed to be benefits from their position in society, but there are also costs. At the same time, everyone will be ready to spend money if his central position in society will bring him great benefits in the end. People often seek to acquire “valuable connections” or want to become “needed” themselves. However, the maintenance of such links requires certain efforts and costs, so that only those links for which the game is worth the candle will actually arise: the benefits exceed the costs.

According to Musatov, in the presence of the above needs in any society, the rule of “six handshakes” arises. This was confirmed by the mathematical model developed by the scientists. Moreover, it works not only vertically, when people look for contacts in power structures through such “handshakes”, but also horizontally, which was previously discovered using the example of people interacting in social networks, where there is no hierarchical ladder.

Why are there six handshakes?

– There was no answer to this question before, while in real networks this is how many handshakes occurred between “agents” in more than 99% of cases. In our model, when chains that are too long appear, there is immediately someone who wants to shorten them.

What makes him do it?

– By bringing the different ends of the chains together, it becomes a useful intermediary, which is considered beneficial in our model. How true this is is a question rather for sociologists or psychologists, but we have shown how a global picture is formed from individual desires and decisions.

Such studies, in the opinion of my interlocutor, can bring us closer to understanding many social processes. For example, how quickly certain ideas, fashion or lifestyle spread in society. Understanding the social network structure is also important for dealing with epidemics.