“Far From A Pop-Science Relic”: Why “6 Degrees Of Separation” Rules The Modern World

Well, maybe you do the best you can. You don’t know the person on the envelope, but you know somebody in their city – perhaps that person can get the message there. At the very least, they can get it to another person, even more likely to know the end reader. Eventually, the message should get there, right?

Perhaps you’d pass such a plan off as overly optimistic, but it has a higher chance of success than you might expect. We are, according to common wisdom, all just six degrees of separation from each other – able, at least in theory, to pass a message from one person to any other in the world with at most five intermediaries. 

It’s certainly a catchy idea, turning up in books, plays, films, and memes throughout the years. But does the math support the motto?

The origins of the idea

The story of “six degrees of separation” begins in a time and place wracked by technological acceleration, economic instability, global isolationism, and a general slide into authoritarianism and fascism. That’s right: we’re talking about Hungary in the 1920s. 

“The population of the Earth is closer together now than they have ever been before,” proposes a character in Frigyes Karinthy’s 1929 short story Láncszemek (in English, Chains) – and “one of us suggested performing the following experiment to prove [it].”

“We should select any person from the 1.5 billion inhabitants of the Earth – anyone, anywhere at all,” the narrator continues. “He bet us that, using no more than five individuals, one of whom is a personal acquaintance, he could contact the selected individual using nothing except the network of personal acquaintances.”

This, as far as anybody can tell, is the origin of the “six degrees” trope – but, as any vaguely philosophical Eastern European author in the 20th century should know, you can’t just put an idea like that out into the world and not expect a mathematician to notice.

“Karinthy’s 1929 thought experiment is already remarkably close to a mathematical hypothesis,” says Iacopo Iacopini, an Associate Professor at Northeastern University’s Network Science Institute, accompanied by his PhD student Leonardo Federici. “[It] is already formulated very clearly as a reachability problem through personal acquaintances, which makes it conceptually ready to be tested even before being formalized mathematically.”

Translation into math

Imagine you have 45 friends, each of whom has 45 friends of their own. Imagine those friends are all in the same situation, all having 45 friends with 45 friends, and so on and so forth. Finally, assume none of these people know the friends of anybody else.

It’s an unlikely scenario, to be sure, but it does prove a point: after six links through this vast network, you would be connected to 45⁶ end points – that’s 8,303,765,625 people, or slightly more than the entire population of the world (for now). In other words, the “six degrees of separation” concept is possible. But is it plausible?

Real social networks look nothing like this.

Iacopo Iacopini and Leonardo Federici 

“[That] calculation is what we call in the field a ‘tree’ structure,” explain Iacopini and Federici – “perfectly efficient on paper and [with] great reachability properties, [but] completely unrealistic for real-world social systems.”  

“Real social networks look nothing like this,” they tell IFLScience.

That’s fairly intuitive, of course: “if you take 45 of your friends, chances are many of them know each other,” they point out. “These loops create redundancy, so instead of having the chain […] described above, you would be going in circles.”

Evidently, a more sophisticated method is required. And, starting fairly quickly after Karinthy’s initial thought experiment, mathematicians started to try just that: “there was this influential work of Erdős and Rényi,” says Renaud Lambiotte, a Professor of Networks and Nonlinear Systems in the University of Oxford’s Mathematical Institute. “It was one of the most influential early works on random graph models, [and] the idea is, basically, each pair of nodes [in the graph] has a fixed probability of being connected, and everything is completely random except for that.”

But as you might imagine, such graphs are as unrepresentative of real life as our trees from before – and, perhaps less obviously, that’s because they’re basically the same structure overall. Once you hit a certain probability, “each node [is] what’s called ‘locally tree-like’,” Lambiotte tells IFLScience. “So, if I look around me, I have a certain number of connections, [and] it’s possible for some of my neighbors to know each other, which that would form a triangle. But statistically – statistically, the graph is large enough it will almost never happen.”

Real social networks, in contrast, are messy and complex. They have “a lot of triangles,” Lambiotte points out; they have celebrities and hermits – “certain nodes [which] are very well connected, and others which are not,” he explains, “which wouldn’t be well fitted by a Poisson distribution.” And none of this gets better over time or scale: “[pioneering network scientist Albert-László Barabási] called it ‘preferential attachments’,” Lambiotte says, but it’s “actually a process that’s been studied for a long time by economists and social scientists – that the rich get richer.”

It all sounds like a recipe for – well, chaos, frankly. But somehow, it kind of all evens out overall. 

“The empirical structure of human relationships is far from simple,” Iacopini and Federici tell IFLScience, but “it doesn’t break the six-degrees phenomenon. It’s the very complexity – the mix of tight clusters, weak ties, and hubs – that makes our world so remarkably small.”

“[It] violat[es] almost every assumption,” they admit. “The fact is that, despite all our clustering and social biases, real networks remain astonishingly navigable.”

Proof in the pudding

In 1967, Stanley Milgram – yes, that Stanley Milgram – set up what should, by all rights, have been a pretty silly experiment.

“The procedure may be summarized as follows: an arbitrary ‘target person’ and a group of ‘starting persons’ were selected, and an attempt was made to generate an acquaintance chain from each starter to the target,” he wrote with co-author Jeffrey Travers in the eventual paper accompanying the experiment. “Each starter was provided with a document and asked to begin moving it by mail toward the target. The document described the study, named the target, and asked the recipient to become a participant by sending the document on.” 

The starters were in Nebraska and Boston; the targets in Massachusetts; the documents could “be sent only to a first-name acquaintance of the sender,” participants were told. In other words, it was the exact scenario we considered right at the top: “each document made its way along an acquaintance chain of indefinite length,” Milgram wrote; “a chain which would end only when it reached the target or when someone along the way declined to participate.”

You’d be forgiven for thinking this experiment simply couldn’t work – and you’d basically be right: out of almost 300 documents that were initially sent out, only 64 made it to their intended recipient, giving a failure rate of more than 88 percent.

That wasn’t the result that caught people’s imaginations, though.

“Within this group [of successes] the mean number of intermediaries between starters and targets is 5.2,” the paper reported. And while it wasn’t Milgram who coined the term “six degrees of separation”, it’s striking how close that result comes to the stock phrase, isn’t it?

The basic idea remains at the heart of a very active and dynamic research field.

Iacopo Iacopini and Leonardo Federici

Modern social networks are even tighter. In 2016, Milgram’s experiment was updated for the Facebook age – the average “degree of separation” between any two of the site’s 1.6 billion users was found to be just 3.57. A slightly smaller figure was found linking Twitter users in 2011; “in the era of social media, the ‘six degrees of separation’ theory [is] a significant overestimation of how hyperconnected our world has become,” Iacopini and Federici say.

And that’s not necessarily a good thing. 

A spider’s web

It may be easier than ever to get a message to some guy in Boston – but, as all three experts point out, our shrinking global network structure comes with significant downsides. Without such close ties, the COVID-19 pandemic may not have spread as quickly or as far as it did: “the virus reach[ed] every continent within weeks, spreading along airline routes that perfectly mirror this hyperconnected and globalized world,” Iacopini and Federici point out. And “it’s not just biological viruses,” they add – “computer viruses exploit similar principles, as do cascading failures in power grids and shock propagation in financial systems.”

It’s precisely this type of problem that has taken “six degrees of separation” from literary musing, through pop-science factoid, to a now thriving scientific field in its own right. Researchers today study not just how starters are connected to targets, but how group chats and viral posts can affect the spread of messages. 

“In a way, the small-world discovery and the research that stemmed from it helped explain crucial phenomena for society,” Iacopini and Federici tell IFLScience. One pertinent line of enquiry, for example, is the rampant spread of misinformation: “We can now trace how false news travels through social media, jumping from cluster to cluster, or how rumors spread through communities,” they say.

While the number itself may be outdated, “six degrees of separation” is “far from being a pop-science relic,” the pair tell IFLScience. “The basic idea remains at the heart of a very active and dynamic research field, which has gradually expanded across disciplines.”

“What began as asking ‘how connected are we?’ in a literary experiment has evolved into a powerful lens for looking at the world,” they say. “[It] provides a framework for understanding not just who we’re connected to, but how connectivity shapes nearly every aspect of our society and the world around us.”