My scale-free contacts
One drawback of returning from Avega’s 2009 conference in Karpathos, Greece, is having a head full of ideas and recharged batteries. It manifested itself a couple of days ago. Around bed time, I felt a sudden urge to map all my contacts, and their connections as well, on the professional network site LinkedIn. Supposedly, I should be able to see the scale-free invariance property of a social network.
That night I went to bed at around 4 a.m. and I was still miles from completing my data gathering. I didn’t finish the next night either – or the next. The fourth night it dawned on me. The very raison d’être for my investigation, the scale-free invariance, was the problem.
Since LinkedIn is a typical social network site, it follows the power law function which, simply put, states that the vast majority of people would have few contacts, but also that there exist a small handful of people that would have lots and lots of contacts.
And so, on the fifth evening, I haven’t finished gathering the data yet. I expect to be done in a week or so, and then I can finally begin automate a solution to connect the dots, so to speak. On the positive side, I have finished connecting my 1st degree contacts, and if they are ordered by number of connections, it’s possible to observe the scale-free invariance pattern – albeit with some minor variance, mainly because the sample set is small. It’s truly remarkable.
As can be seen, I’m missing a person; preferably, one with a really huge number of contacts. And more than 500 of those would be nice. This would fix the vertical asymptote that breaks off at around 325 instead of going straight up. I’m not worried though, because the nature of the power law itself also states that, in time, such a power law-conformant person will emerge.
The center of the universe is… me
In my small universe on LinkedIn, I’m the only one that knows everyone else. While some of my contacts know each other, along with some people outside my network, it’s not the case that everyone knows everyone else in my network, i.e. my network is not a complete graph.
In case you're wondering, I’m the dot labeled “29” that sits in the middle and connects the two big clusters of people to the left and to the right. I should mention, that the labels on the dots indicate the number of people that each person knows in total. Also, I have sized the dots relatively and accordingly.
There really isn’t much interesting to say about this small universe, except from the fact that if a person from the left side connects to a person from the right side, I will be rendered utterly worthless as a broker between small worlds .
As I mentioned earlier, I expect that in a few weeks time I have gathered, automated, and analyzed enough data from my contacts and their connections to write a follow-up. Then we can begin to talk about all kinds of interesting things, like for instance the best way to vaccinate an entire population against the hyped swine-flu, with the fewest possible vaccines.
References
- Albert-Laszlo Barabasi, Linked: How Everything Is Connected to Everything Else and What It Means, Plume, 2003
- Brian Uzzi & Shannon Dunlap, Managing Yourself: How to Build Your Network, Harvard Business Review, December 2005
- Kurt Mehlhorn & Peter Sanders, Algorithms and Data Structures: The Basic Toolbox, Springer-Verlag, 2008
- Malcolm Gladwell, The Tipping Point: How Little Things Can Make a Big Difference, Back Bay Books, 2002
- Rob Cross, Jeanne Liedtka & Leigh Weiss, A Practical Guide to Social Networks, Harvard Business Review, March 2005
Postad av Martin Kaarup
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Kategorier:
Graph Theory
Scale-free Networks
Self-organization
