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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September 26, 2008 » 01:57 PM

From an interview with ethnobotanist and anthropologist Wade Davis:

One of the cultures you celebrate in Light at the Edge of the World is the Inuit. What do you most admire about them?

Davis: The Inuit didn’t fear the cold; they took advantage of it. During the 1950s the Canadian government forced the Inuit into settlements. A family from Arctic Bay told me this fantastic story of their grandfather who refused to go. The family, fearful for his life, took away all of his tools and all of his implements, thinking that would force him into the settlement. But instead, he just slipped out of an igloo on a cold Arctic night, pulled down his caribou and sealskin trousers, and defecated into his hand. As the feces began to freeze, he shaped it into the form of an implement. And when the blade started to take shape, he put a spray of saliva along the leading edge to sharpen it. That’s when what they call the “shit knife” took form. He used it to butcher a dog. Skinned the dog with it. Improvised a sled with the dog’s rib cage, and then, using the skin, he harnessed up an adjacent living dog. He put the shit knife in his belt and disappeared into the night.

September 25, 2008 » 11:21 AM
“Video from a camp north of Toronto in December 2005 shows a car spinning around in a nearby, snow-covered parking lot. Prosecutors characterized that as special driver training but the defense, and many outsiders, said it was nothing more than “cutting doughnuts,” a favorite winter pastime of young Canadian motorists.” - A key piece of evidence submitted in the trial of a gang of alleged young Canadian terrorists.

September 24, 2008 » 11:21 PM
“Life imitates art imitating life: just thought a gnat crawling across my monitor was part of a Flash-based ad. I clicked it.” - A Tweet from Bill Braine.

September 24, 2008 » 02:37 PM
“Funniest FB friend request ever: “Twitter friend hoping to get to second base (Facebook!) ;-).”” - A recent Tweet by Pistachio

September 24, 2008 » 12:28 PM
Chinese powdered-milk crisis creates a new market: The return of the wet nurse

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