Six Degrees of Separation: Do We Really Live in a ‘Small World’?

Arguments about the interconnectedness of human society have received a shot in the arm with the publication of a study of 30 billion instant messaging conversations between 240 million people around the world.

Microsoft researchers claim their results support Milgram’s idea that each of us is only ‘six degrees of separation’ away from anyone else on the planet.1

It was back in the 1960s that social psychologist Stanley Milgram found that he could send a letter to a random person in Nebraska or Boston and have it reach a random target person in Massachusetts.

The letter asked the first random receiver to forward it to someone who might be more likely to know the target person, but it had to be someone they were on first-name terms with. So, for example, if the first recipient, who lived in Nebraska, knew anyone at all in Massachusetts, they would send it to them. Then on and on it would go until it reached the target.

Milgram found that on average it would take 5.2 intermediaries for his letter to go from the first person to its destination, via each person’s social network.

Six degrees of Kevin Bacon and Paul Erdos

Milgram took this study, along with other research, to demonstrate that we really do live in a small world. Milgram’s work eased itself into the popular imagination with it’s optimistic message that each of us is only a few social steps away from everyone else in the world.

The theory inspired the trivia game ‘Six Degrees of Kevin Bacon‘ in which participants try to link any given actor back to an appearance with Kevin Bacon in as few moves as possible. Mathematicians also have a version in which they trace each other back to the eccentric Hungarian mathematician Paul Erdos through shared publications.

Milgram’s work has been challenged, though, by Professor Judith Kleinfeld who found, when re-examining Milgram’s work, that there were problems with his method. For example he used relatively prominent people in society as the start and end points for his chain letter, plus a very high percentage of letters never arrived at their destination at all. Subsequent replications of Milgram’s work are also few and far between and don’t test links across class or geographical boundaries.

Kleinfeld points out that Milgram’s claim for the six-degrees of separation could be an academic myth. Real life is probably not as incestuous as the worlds of actors or mathematicians.

Small world of email

In 2003, though, some support for Milgram’s idea was found by Duncan Watts and colleagues at Columbia University, in a paper published in Science. Emailers were asked to try and forward a message to one of 18 target people in 13 different countries, going via their friends and acquaintances. All together more than 60,000 people took part. They found that successful chains were completed in between 5 and 7 steps, similar to Milgram’s results.

Unfortunately this email replication had the same problem as Milgram’s original study – many chains simply broke down. Also, like Milgram’s study, the targets were relatively visible in society, one was a vet, another a policeman, another a technology consultant. Where are the factory operatives or convenience store workers in this sample?

New study: 6.6 degrees of separation

But a new study carried out by Leskovec and Horvitz for Microsoft Research addresses some of these points since they used data that cuts across geographical and class boundaries. They analysed data collected by Microsoft from 30 billion instant messages sent around the world in one month in 2006.

Examining this data – the largest social network ever analysed – they found that the average number of hops between any two instant messenger users was 6.6 – slightly higher than Milgram’s finding.

Leskovec and Horvitz claim their work supports Milgram’s theory that each of us is only separated from anyone else by six jumps. The problem, though, is that it is hard to generalise from an online to an offline environment. People behave differently online than they do offline:

  • The biggest problem is Leskovec and Horvitz’s assumption that instant messaging between two people can be considered a marker of a relationship. For example, I speak to the postman but he’s not really part of my social network – certainly not in the sense Milgram meant. The data is likely to over-estimate how much instant messaging between two people can be considered a marker of a ‘relationship’.
  • A related problem is that people are more disinhibited online. They are more likely to say or do what they want rather than feel social pressure to keep quiet or conform. Consequently people may be more likely to talk online to people through instant messenger that in the real world they wouldn’t. This could easily inflate online social networks.

These are just a couple of the main problems – others include a skew towards younger people and the data, by its very nature, only taking into account more highly developed, computer-literate groups in society.

Small world?

There are all sorts of reasons that we may want to believe Milgram’s small world conclusions, as Kleinfeld herself points out. If we really are so easily connected to others our lives seem less isolated, cold and forbidding.

Both Milgram’s and Watts and colleagues’ studies seem to support the small world theory but it is hard to draw solid conclusions when so many chains of communication broke down in both studies. It’s difficult to know whether these chains were broken because of apathy or because the messages reached a cul-de-sac in a social network.

It’s probably over-stretching the new research by Leskovec and Horvitz to claim it supports Milgram’s idea of six (or seven) degrees of separation in the offline world. We’ll have to wait for an equivalent offline study before we can truly say it is a small world. Until then we’ll have to be content with playing Six Degrees of Kevin Bacon (and Paul Erdos for mathematicians) which rely on much more intimate social networks.


1Milgram himself never used the phrase ‘six degrees of separation’.

[Image credit: social d]

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Published: 5 August 2008

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