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!)
Posted by Clive Thompson at October 23, 2005 09:53 PM
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Interesting indeed.
for me those "superconnectors" are the big mystery, that make so many things move, and, part of it, will remain unknown, won't it...isn't it a part of the chaos theory?
Posted by: Moon River at October 24, 2005 4:52 AM
I wonder how much of that difference of opinion might turn out to actually be a difference of medium - basing a netwroking study on email could give wildly different results to basing a study on verbal messages, and so on. Would the most 'human' study be one which just specifies a message, and allows any medium of transmission deemed fit by the participants?
Posted by: Tony at October 24, 2005 7:09 AM
Just to be really boring, I'd like to point out that the internet basically works this way - all the routers are the 'superconnectors', and they all have maps of all other routers, and each member has published who their local router is, so it goes from me, to my superconnector, to your superconnector, to you.
The email six degrees result probably has more to do with how we route than how we're connected. Most people probably interpret the rules of the passing along to view sending through a superconnector as cheating, since everybody knows that will work, and besides, superconnectors tend to be very busy, you only use their connectivity for something really important. This is why routers do nothing but route - being a superconnector can make you be a bottleneck very easily.
Posted by: Bram at October 24, 2005 9:39 AM
Bram, good point about the social problems of being a superconnector -- you get pinged to death. Probably why so many CEO superconnectors keep a phalanx of attendants around them -- to prevent connections, as much to enable them.
Tony, yeah, you wonder what biases are introduced by the email-only paradigm. Obviously, Watts picked email because it's uniquely easy to track, and thus produces very clean data, experimentally. But I too would wonder what sorts of pathways a media-agostic message would take!
Moon River, ya got me.
Posted by: Clive at October 24, 2005 2:29 PM
Superconnectors might make connections easier, but according to Jane Jacobs, they can ruin the connection game. She and her sister used to play a game about getting a message from one person, say in upland New Guinea, to another, say in upland Sicily, and they used to have a lot of fun figuring out possible routings. Then, along came Eleanor Roosevelt, and she traveled everywhere, and she knew everyone. She also ruined their game. It was like playing poker with a dozen jokers wild in the deck. Not only could the game be played without Eleanor Roosevelt, it had been a lot more fun.
Posted by: kaleberg at October 27, 2005 12:28 AM
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Interesting indeed.
for me those "superconnectors" are the big mystery, that make so many things move, and, part of it, will remain unknown, won't it...isn't it a part of the chaos theory?
Posted by: Moon River
at October 24, 2005 4:52 AM
I wonder how much of that difference of opinion might turn out to actually be a difference of medium - basing a netwroking study on email could give wildly different results to basing a study on verbal messages, and so on. Would the most 'human' study be one which just specifies a message, and allows any medium of transmission deemed fit by the participants?
Posted by: Tony
at October 24, 2005 7:09 AM
Just to be really boring, I'd like to point out that the internet basically works this way - all the routers are the 'superconnectors', and they all have maps of all other routers, and each member has published who their local router is, so it goes from me, to my superconnector, to your superconnector, to you.
The email six degrees result probably has more to do with how we route than how we're connected. Most people probably interpret the rules of the passing along to view sending through a superconnector as cheating, since everybody knows that will work, and besides, superconnectors tend to be very busy, you only use their connectivity for something really important. This is why routers do nothing but route - being a superconnector can make you be a bottleneck very easily.
Posted by: Bram
at October 24, 2005 9:39 AM
Bram, good point about the social problems of being a superconnector -- you get pinged to death. Probably why so many CEO superconnectors keep a phalanx of attendants around them -- to prevent connections, as much to enable them.
Tony, yeah, you wonder what biases are introduced by the email-only paradigm. Obviously, Watts picked email because it's uniquely easy to track, and thus produces very clean data, experimentally. But I too would wonder what sorts of pathways a media-agostic message would take!
Moon River, ya got me.
Posted by: Clive
at October 24, 2005 2:29 PM
Superconnectors might make connections easier, but according to Jane Jacobs, they can ruin the connection game. She and her sister used to play a game about getting a message from one person, say in upland New Guinea, to another, say in upland Sicily, and they used to have a lot of fun figuring out possible routings. Then, along came Eleanor Roosevelt, and she traveled everywhere, and she knew everyone. She also ruined their game. It was like playing poker with a dozen jokers wild in the deck. Not only could the game be played without Eleanor Roosevelt, it had been a lot more fun.
Posted by: kaleberg
at October 27, 2005 12:28 AM