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Tim Worstall Contributor


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19 Degrees Of Kevin Bacon: Just How Small Is The Web?

An interesting little finding from some Hungarian scientists: any one page on the web can be reached from any other by a maximum of 19 clicks. It’s another demonstration of small world theory and as with that it depends upon a few certain places being “super-connected“.

At first glance, the web may appear to be an almost random mass of information.

However, researchers say that in fact,there is a ‘Kevin Bacon’ effect – meaning any web page is connected to any other by just 19 clicks.

The statistic echoes the famous ‘Six degrees of Kevin Bacon’ game, which claims anyone on Earth can be linked to the actor through just six people.

That’s the Mail there and of course they’ve managed to slightly garble that basic theory. What we’ve actually got here is two slightly different things: that anyone in the world can be linked to anyone else with only six degrees of separation. Then there’s also the Kevin Bacon game which is an example of this within the movie industry. They both work, as does the 19 clicks from one web page to another, on the idea that some links are “super connections”.

In the link from any one person to any one other it depends on the manner in which some people are connected to vast numbers of others. For example, to get from me to Ronald Reagan is pretty simple. My father once had a job that reported to the UK Cabinet, which means he met Margaret Thatcher. Thatcher to Reagan is obvious. But of course being linked to either Thatcher or Reagan means being linked to pretty much every world leader of the 80s and or 90s. It’s only one more degree to Yeltsin, or Deng, or the Dalai Lama. You can see how any link to such a super connected person immediately puts you in touch with millions upon millions with only one or two more degrees of separation. And the fact is that pretty much all of us are indeed within two or so degrees of separation with such a super connected person: thus the only six degrees of separation between any two people.

With the Kevin Bacon game Bacon himself is an example of such a super connected person. The aim is to link any two actors through movies that they have appeared with the same people in. So, if (a made up example ) Charlie Chaplin was in a movie with John Huston who was in one with John Wayne then there’s two degrees of separation between Chaplin and Wayne. The value of Bacon here is that he’s one of those super connects: he’s been in a lot of movies with a lot of different people. and we find that it’s very difficult indeed to find two actors in the IMDB movie database that we cannot link in those six moves.

In the sciences we’ve another example with the Erdos number. Paul Erdos was an extremely prolific scientific collaborator. The link here is who has written a paper with whom? An Erdos number of one means that you wrote one with Erdos himself, two with someone who wrote one with someone who did and so on. There’s even the combined Erdos Bacon number, of the separation between an actor and Kevin Bacon and a scientific paper with a collaborator of Erdos: Natalie Portman has a surprisingly high number here.

The underlying structure of all of these relationships is that they do depends upon those super connectors. And the same is true of the web itself: places like Google and Facebook are the obvious connectors. And to be honest, I’m not sure we should be all that surprised either. Given that Google (and the other search engines) are deliberately attempting to catalogue the web I don’t think it’s all that amazing that they are indeed those super connectors.

But still, only 19 degrees of separation over the whole web: pretty small, hunh?

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  • judge judge 1 year ago

    “Natalie Portman has a surprisingly high number here”. I think you probably mean she has a surprisingly low number – low being more connected!

  • Tim Worstall Tim Worstall, Contributor 1 year ago

    You are entirely correct. “Low number” or “high ranking”. Given a simple binary choice I manged to mangle it.

    Ho hum. I shall report to re-education immediately.