‘Six degrees of separation’ phenomenon proven by mathematicians to be true!

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.

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Comments

  1. But that’s just within a select group of people called ‘social media users’. Try that with fishermen on the Baikal and Kalahari tribesmen or basket weavers in a Peruvian village. The only reason this works is the vast ‘phoney friends’ networks we’ve built in the last 20 years. We don’t actually have real relationships with almost any of the network participants.

    1. Good post. I never would have thought of any of that about the socially-isolated groups. On the other hand, some of those Kalahari tribesmen and some of the those Peruvian villagers must know at least one person outside their group, so ….

      1. Ya, you never thought about doing some simple multiplication either.

        Americans are incapable of doing grade school math.

    2. If you could actually do some trivial high school arithmetic you could prove it yourself.

      But you can’t.

  2. WE all have discovered this through normal conversation and networking. It does not take much to know someone who knows someone.

  3. We hosted 14 exchange students, AND we have traveled extensively in our long lives. So many times, we found connections with others through the people we already knew. Once, one of my exchange kids from Brazil, was visiting London and struck up a conversation with a man who happened to be the next door neighbor to one of my brothers, who this boy knew well. I’ve always thought however such connections form in social circles where people travel frequently and are of similar socio-economic backgrounds. Yet, this occurs with people we run into who are not well traveled, or have anything to do with our backgrounds. It is fascinating and this was an interesting read.

  4. “mathematics that shape our small world….. power of six degrees …. the magic of six degrees.”

    The authors have it backwards. It is human nature that determines the 6 degrees, not mathematics. The 6 degrees is a mathematical observation of human behavior, not an effect of mathematics ON human nature. Mathematicians have not proven anything; they have just observed and drawn a conclusion based on data collected.
    It is “mathematics that describe our small world….. no power…..no magic.”

  5. So if I tell someone, I know the short position on Gamestop has not closed and they can make money on the short squeeze. That information should spread like wild fire. DRSGME.org

  6. When mathematicians “prove” something, there’s typically math involved; this article contains none (the word “math” contains a link to article about board games!). Is “about 6” degrees 6.0, or 5.8, or 6.3, or what? How was it determined? Does it change with population size? How? This garbage is about as intellectually rigorous as a bowl of applesauce.

  7. This actually does work. It’s how I found out that the short position did not close on Gamestop. A friend of a friend told another friend and they will be in on the short squeeze

  8. A non-American grade 9 student might think about things and come to the conclusion that the average person knows about 25 people.

    They will know about 25 people and so on.

    So the network of connections will be approximately 24^6 = 200 million approx.

    There.. Proposition “proven”. It’s magic. No one in America can figure it out.

    Just flush the entire country. It is worthless.

  9. The use of the term “degrees” is not appropriate here. The term should be “levels” or “layers”.

    In the physical world 6-degrees of freedom, movement, or separation are defined as: pitch, roll, yaw, heave, surge, and sway.

    And in terms of network sizes, any number greater than 1 to the sixth power is always a big number.

  10. It’s amazing how, in the U.S., it’s so easy to know someone that opens you up to a vast network of “important” contacts. Have you met your local sheriff? There’s a good chance that puts you 2 steps from the governor. Ever been in the military? That encounter with the base commander, likely a bird colonel, puts you 2 steps from the joint commanders and 3 steps from the president. How about a professor? Depending on the discipline that could connect you to many of the foremost scientists in the country, making it just 3 steps to scientists in half the countries in the world.

    6 degrees may not connect everybody to everybody, but I’d wager that it connects most of the world.

  11. So I know a guy, that knows a guy, that knows a guy, etc. that knows a billionaire. What good does that do ME? I don’t know the person. I can’t call them up and borrow a couple of dollars. We aren’t going to hang out together. Chances are that the only one in the chain that knows said “Billionaire ” does not even know I exist let alone give a damn about me.
    This just proves how pathetic we have become, that we live our lives trying to pretend that we are more than we really are, or will ever be.

  12. The phenomenon is interesting, whether proven to the degree wished for by some of the posters.
    The rude and impolite remarks simply make any subsequent postings by the individuals
    less credible.

  13. Im sorry, but the idea of people randomly passing a package around and it finds its recipient in six tries is ludicrous.

  14. I don’t really care what the results are when the premise is faulty:

    People naturally seek prominence in social networks, strategically choosing connections that place them in central positions.

    Maybe if you’re a narcissist, this applies.

  15. OK, this reminds me of germ theory. Let’s say there is a door handle on a door in a busy location, for example a restroom in a New York subway station. We already know that if a person touches that handle with germy hands; everyone who touches it the rest of the day will pick up those germs. Then each of those people touch other door handles, etc. Before you know it you have a hell of a lot of contaminated hands with only the connection of door handles in busy locations. This is how pandemics happen. As the day progresses you have exponentially bigger circles of contaminated hands. You can stick these numbers into all kinds of equations to fit your theories. I could argue that it took any random number of iterations and logically it would be true as long as it is a large enough number to move the process along quickly enough to actually study. This has been applied, erroneously to sexual behavior. We are told that if you have sex with someone, in terms of epidemiology you are actually having sex with everyone they ever had sex with. Pretty sure this is a sort of scare tactic to promote abstinence or at least condom use; since you could not dependably find the DNA, nor necessarily the pathogens of those previous sex partners within the sex organs of that partner.

  16. As a very ordinary person, I have connected with extraordinary people just through my own friends and associates. For instance I drove to a cocktail party with Madame Chennault given in her honour by two former military officials of Chiang Kai Shek’s Nationalist Chinese army and navy, a general and an admiral ( the grandparents of my girlfriend at the time). Much later I met the cousin of the King of Thailand. I also had lunch with the husband of Adnan Kashoggi’s daughter who was a cousin of Dodi Al Fayed, Princess Diana’s boyfriend. His brother worked in our small office so we were in contact on occasion. Their mother in London was first cousin to Aristotle Onassis. There are more such connections in my life but this should be enough to prove the point being made in this bog.

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