The Science of Six Degrees of Separation

I have a friend named Sammy who, back in the early 2000s, wrote some code for his MySpace page. And what the code did was anybody who visited his page would have his picture and a tagline that said, “Sammy is my hero,” copied over to their homepage. And that was a bit of fun for a while, but Sammy wanted more. And so, he tweaked his code so that not only the picture and the tagline were copied over, but also the code itself. And now it exploded.

In just nine hours, he had reached 480 accounts. In 13 hours, he was up to 8800. And in just over 18 hours, he had hit a million accounts, which was a full 1/35th of all the accounts on MySpace at the time. So, in a panic, he tried to delete his page. And when he was successful, he actually took down the whole of MySpace with it. He was arrested and convicted of computer hacking and ordered not to touch a computer for the next three years.

But I think what this story really tells us is just how connected we all are. Imagine you have 44 friends, and each one of those friends has 44 friends who are not also your friends. And each of them has an additional 44 friends, each of whom has 44 friends, who again has 44 friends, and they have 44 more. Then, in a chain of just six steps, you would be connected to 44 to the sixth, or 7.26 billion people, more than are alive on Earth today. And we have contemplated how closely connected we are since long before MySpace even existed.

Back in 1929, a Hungarian author and poet named Frigyes Karinthy wrote a short story called "Chains." And in it, one of the characters challenges the others to find another person on Earth that he cannot connect himself to through fewer than five intermediaries. This is the origin of six degrees of separation. If the theory is correct, it means that you would be connected to the Queen or Tom Cruise in just six steps. But they may be the easy ones. What about this shop owner or the Mongolian sheep herder?

What the theory really means is that any two people picked at random from anywhere on the Earth would be connected by just six steps. The idea remained just fiction until, in the 1960s, a Harvard psychologist, Stanley Milgram, attempted to test it. He called it the small world experiment after that phenomenon where you are at a party, you meet a stranger, and you find out that you have a friend in common, and you remark: “Oh, it is such a small world.”

What he did was he sent out 300 packages to people both in Boston and in Nebraska. Now, what he wanted those people to do was try to send their package to a target person in Boston, but they weren’t allowed to send it directly to him. They had to send it to someone they knew on a first-name basis who they thought had a better chance of knowing the target, and they could forward it on in the same way.

Now, as you might expect, most of the packages never made it, but 64 did, and the average pathway was 5.2. So now, six degrees of separation had experimental confirmation. Or did it? If you look more closely at Milgram’s sample, you will find that of the 300 people, 100 were located in Boston, the actual city where the target lived. Another 100 were stockbrokers, which was the same profession as the target. So only 100 people lived in a different state and had a different job. And of them, only 18 of their packages made it to the target.

So we are talking about a sample size of 18 as all the evidence there was for six degrees of separation. So, experimental evidence was tough to come by. But a decade earlier, a mathematician named Paul Erdos had tried to work out the theoretical properties of networks like these. But he didn’t have any information on the structure of real social networks, so he decided to work on networks where the connections between nodes were all completely random.

And we can actually simulate a network like this using buttons and thread, where we just connect up the buttons at random. What Erdos found is that when the number of links per node is small, the network is fragmented. Pick up any button, and few others will come with it. But once you exceed an average of one connection per node, the behavior of the network changes dramatically. They almost all link up, forming a giant cluster. Now, if you pick up any button, almost all of the rest will come with it.

This change happens rapidly, and it resembles a phase transition in physics. Now, you could call this a small world network since the path between any two buttons is short. The thing about random networks is that they are naturally small world networks because you are just as likely to be connected to someone here in Manila as you are to someone in your own town. But obviously, a random network doesn't represent real life very well. So, what do real-world networks look like?

Well, for that, we need to go to the empirical data. In 1994, a couple of college kids invented a game called six degrees of Kevin Bacon in which you try to connect any actor to Kevin Bacon through just six steps through his co-stars. Now, a couple of sociology researchers got access to their database of a quarter million actors, and they analyzed the network, and what they found was that it was a small world network, meaning between any two actors, there were only a very small number of steps. And that is very similar to a random network.

But unlike a random network, the actor network also showed a high degree of clustering; that is, they often worked together in small groups. So how do you get both this grouping behavior—a high degree of clustering—and the short number of steps between any two actors? Well, to figure this out, they looked at two different extremes. Imagine a circle of nodes. Now, if you connect them at random, you get the same outcome as Erdos: short paths between any two nodes, but little clustering.

Now consider connecting up the nodes only with their nearest two neighbors on each side. Now, clustering is high, but path lengths are long for two nodes picked at random. But what if you take this setup and rewire just a small number of connections randomly? What you find is that the path length drops rapidly, but clustering still remains high. So, the key to modeling real social networks is to have a lot of clustering behavior—that is, your friends are also friends with each other—but also to have a few random acquaintances.

And the importance of those acquaintances can’t be overstated. There was a researcher named Granovetter in the 1970s who published a paper called “The Strength of Weak Ties,” in which he points out: You are much more likely to get a job through those random acquaintances than through your close friends. And if you think about it, that makes sense because you and your close friends all know the same people and have the same information. It is through the random acquaintances that you can get connections with people very far from your social circles.

So, you can find new jobs, new places to live, and you can be connected to the outside world. So, in fact, it is those random acquaintances that make possible six degrees of separation. So when I want to...

I am told the degrees have dropped in recent years.

Really?

...to like four degrees.

Tell me about that. How do we know this?

I don’t know how they measure it, but I have tested it, and I think it actually has dropped based on how many people have friended one another on Facebook. The friendship circle has grown, not that they are bosom buddies, but they are people you have access to. That is the point.

Right.

And it is... do you know this person who then knows that so that I have access to these other people? So I am told that it has dropped. As much as the six degrees, we are down to four, at most five.

I think Neil DeGrasse Tyson might be right. In 2011, Facebook analyzed their data, and they found that 92 percent of their users were connected through just five steps. And that number is decreasing over time. The concept of six degrees of separation has fascinated people for nearly a century. And I think that is not only because of how counterintuitive it is, but also how comforting it is to know how closely we are all linked, not in some kind of abstract, ill-defined way, but through hard scientific data. Just six handshakes will connect you to anyone else on the planet.

Now, I have a challenge for you. In the spirit of six degrees of separation, I want to try an experiment. I want you to try to get an email to me. But you can’t send it directly to me unless you know me. So, assuming you don’t, I want you to send it to a friend of yours, someone you know on a first-name basis who you think has a better chance of getting that email to me. If your email eventually gets to me through a chain of people, I will send you a postcard in the mail, and I will tally up if we were able to get that done in six links or not. So, let’s try to do it and see if we can connect.

The instructions are in the description. This episode of Veritasium was inspired by the Fine Brothers, Ben and Rafi Fine, who are friends of mine. So we are connected through just one degree of separation. Now they have a brand new TV series launching on TruTV. It is called “The Six Degrees of Everything,” and it is a fast-paced comedic show that tries to show us how six things that we don’t think are connected actually are. It involves sketch comedy and songs and reality TV.

I am really looking forward to seeing how they are going to do this. So you can check it out Tuesdays at 9:30 or 8:30 central on TruTV. I am so looking forward to it. And thank you to the Fine Brothers for sponsoring this episode so I could check out the science of networks.