Sunday, September 05, 2010

Six Degrees, and How I Met You

In his book, "The Tipping Point", Malcolm Gladwell outlines the three key factors that will create the tipping point for an epidemic - the mass spread of something; whether it be virulent, informational or whatever.

The first of these factors is the Law of Few - the idea that a small proportion of a population will have a disproportionately large effect on it.

In discussing this, Gladwell brings up Stanley Milgram's "Small World Experiment" - i.e. the Six Degrees of Separation phenomenon.

Intuition tends to lead us to believe that it can't possibly be so that everyone can be linked by so few connection. But in fact, what you find is that what makes the six-degrees possible is the existence of 'connectors' - a (relatively) small collection of people who are connected to a disproportionately large number of people.

And it's because of these connectors that we can find short routes (six degrees or less) between any two individuals - despite how disconnected they may seem.

In the case of Twitter, if we assume that a connection between a pair of individuals only has to be one way, the degree of separation between users is surprisingly small.

"the average path length is 4.12 with 93.5% of people within 5 or fewer hops of everyone else" [source]

This is almost entirely on account of celebrities. I mean, over 5million people have a maximum separation of degree 2, thanks to being followers of Bieber. But the less said about him the better.

The Point is, celebrities ruin everything.

To demonstrate the "Law of Few", Gladwell offers the following exercise - list 40 of your closest friends. Work backwards through them to determine through whom you met each of them.

What you will tend to find is that a majority of those links pass through 1 (or a very small number) of those friends - the connectors.

Obviously, I had to try this for myself. I decided to go with my Twitter follows; it follows on from previous posts, I've already done a lot of the leg work in those posts, and because you people are likely to care more if you're involved.

So I tried to recall through whom I met everyone (some before or outside of Twitter). I'll admit, it may not be perfect - my memory is only so good.

[Edit] - Interactive ManyEyes version here

So for example: I met Alex in primary school. Through him I met Sally, and through Sally I met Amy. Through Amy I met Joe (PkmnTrainerJ), and through Joe I met Aerliss, CatfoodJackson and ZeRootOfAllEvil.

It's also important to note that this ignores how other people in my network were introduced to each other, and ignores anyone that I may have introduced to someone else.

For an example of the first point: to the best of my knowledge Alex met Sally through his then girlfriend Lottie (though I don't know how they each met Lottie). Sally met Amy through George (and again, I'm not entirely sure how they each met George). Amy met Joe on Fanpop. And I have no idea how Joe met everyone else. But feel free to fill in any gaps.

And for an example of the second point: I met Craig (shinelikestars6) randomly on Twitter (to the best of my recollection), and introduced him to Sally.

So it's a complex network overall. But all that matters for the above is how I met everyone.

So you should be able to see from the graph that the major connector is Amy - being responsible for me meeting 9 of the people in this network. Joe would get second place, and joint third would go to Andrew (abooth202) and Craig.

And for all I know, other people on the graph may be connectors for other people - this would possibly be reflected in their follows/followers numbers. They're just not represented as such on my graph.

And while I may appear to be a connector myself, that's more to do with the fact this graph is centred on me.  At most, I've introduced maybe two pairs of people, if that.

But going back to the six degrees, everyone in my network is connected to each other by at most two degrees of separation (by way of me) - despite the fact that some of them may not be aware of some of the others' existence.

And a good demonstration of this within my network is that missgiggly in Australia is only 2 degrees away from Aerliss in Scotland. And as a side note, I came to know both of them mostly by virtue of us all being Doctor Who fans.

So as Gladwell summarizes:
"These people who link us up with the world, who introduce us to our social circles - these people on whom we rely more heavily than we realize - are Connectors, people with a special gift for bringing the world together."
For more on the subject, read his book. I'd recommend it.

And if you want to make your own graph and would like help, feel free to ask.


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