The solution to the “six degrees” problem

Many people have heard of the famous “six degrees” experiment, in which psychologist Stanley Milgram asked individuals in Boston and Omaha, Neb., were asked to deliver a letter to a target stranger in Boston, using only a chain of acquaintances: You’d pass the letter to someone who might be closer to the target, and they’d pass it on, and so on. Milgram discovered that on average, it took roughly six links to get the letters to their destination.

A cool finding, indeed. But got network scientists wondering: Is there an algorithm that could scan a network and automatically deduce the fastest possible route for a message? If you had, like, 4,000 nodes all loosely and chaotically joined, could one algorithm grok the speediest way to get from any point A to any other point B?

It sounds pretty abstract, but this science has a lot of practical applications. Wifi “mesh” networks, for example — which I wrote about last month — could work much more quickly and efficiently if the mesh “knew” the fastest route for a message to travel. And it might be possible to stop computer viruses and worms in their tracks if one could automatically intuit the fastest route between computers online. So for years, scientists have developed various solutions that map out networks, with varying degrees of success.

Now two researchers at the University of Amherst have published what appears to be the best algorithm yet — and it’s based on human psychology. As they note, our connections in society aren’t random; we tend to know people based on shared charcteristics: Dentists know other dentists, Upper East Siders in Manhattan know other Upper East Siders, sixth graders know sixth graders. And then they point out the observation that Malcolm Gladwell made famous in The Tipping Point: That certain rare people seem to have a lot more connections than other people — “superconnectors”, as Gladwell calls them. So, as a press release on the research notes …

This “degree disparity” leads to some individuals acting as hubs.

Taking these factors into account simultaneously results in a searching algorithm that gets messages to the target by passing it to gregarious individuals who are most like the target.

They called their new algorithm “expected-value navigation”, or EVN. When they tested it against several pre-existing, popular algorithms, it worked better — producing shorter, more efficient pathways. (It’s the top one in the chart above, which is taken from their PDF paper on the subject.)

Here’s the interesting thing, though. Ever since Gladwell’s book, people have assumed that “superconnectors” are crucial to the transmission of messages and information through society. As Gladwell argued, if it weren’t for those ultrapopular, massively gregarious people, memes wouldn’t spread as quickly through mass culture; indeed, hunting down and targetting the ultracool, early-adopting superconnectors of the teen-and-youth world has been the holy grail of marketers for years now. And this study would seem to affirm that superconnectors are the glue that holds social networks together.

But other research suggests they really aren’t so crucial. Duncan Watts, another famous network researcher, has spent years replicating the “six degrees” study by using email — which allows him to carefully study the role of each node in message propagation. His conclusion? Superconnectors may well exist — but they don’t matter. Messages travel through society in a surprisingly democratic fashion, relying most often on “weak” and “intermediate” nodes instead of superconnected ones.

Curious, eh?

(Thanks to Robots.net for this one!)


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I'm Clive Thompson, a writer on science, technology, and culture. This blog collects bits of offbeat research I'm running into, and musings thereon.

Currently, I'm a contributing writer for the New York Times Magazine and a columnist for Wired magazine. I also write for Fast Company and Wired magazine's web site, among other places. Email or AOL IM me (pomeranian99) to say hi or send in something strange!

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The “Milky Way Transit Authority” map

Should automobile software be open-sourced?

My Bookforum review of Jaron Lanier’s “You Are Not A Gadget”

Molecular secrets of the “iron-plated snail”

Garry Kasparov, cyborg

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a bunch of stuff

January 31, 2010 » 07:29 PM
V. A. To me death seems to be an evil.
M. What, to those who are al­ready dead? or to those who must die?
A. To both.
M. It is a mis­ery, then, be­cause an evil?
A. Cer­tain­ly.
M. Then those who have al­ready died, and those who have still got to die, are both mis­er­able?
A. So it ap­pears to me.
M. Then all are mis­er­able?
A. Ev­ery one.

January 24, 2010 » 03:22 PM

One of the more interesting trends is family, which came in at number five. Specifically, discussion about family, moms, dads, daughters, etc. jumped during 2009. With Facebook users getting older, this isn’t a big surprise. However, the fact that the mention of “kids” jumped by a factor of five this year is rather dramatic. It’s tough to know what this means, though. (via Facebook Unveils Most-Mentioned Topics of 2009

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January 15, 2010 » 01:36 PM

BEYOND AWESOME. They are announcing a recall of the Plush Uterus “due to a potential choking hazard for children”. To apply for it, “Please send an email to the address below with the subject line, ‘UTERUS OPT OUT’”.

January 14, 2010 » 10:04 PM

“To order, please TYPE “YES” IN CHECKBOX BELOW TO AGREE YOU UNDERSTAND THIS PLUSH MUST BE KEPT AWAY FROM KIDS (it is a sex organ, after all). If it is not checked, WE WILL NOT SEND THE UTERUS.” (via @ibogost)

January 11, 2010 » 01:45 PM

I watched Space: 1999 back in the day, but I swear to god I do not remember this scene.

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