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Detecting Patterns in Complex Social Networks
Roland Piquepaille writes "So-called social networking is very popular these days, as show the proliferation of services like Friendster, Orkut and dozens of others. But do the companies behind these services have any idea of what is hidden inside their complicated networks? When these networks reach a size of millions of users, it's not an easy task. A researcher at the University of Michigan is trying to help, with a new method for uncovering patterns in complicated networks, from football conferences to food webs. This overview contains more details and references about this non-traditional method. It also includes a spectacular representation of the Internet and another image showing a food web at Little Rock Lake."
I remember the first maps of the Internet showed that certain nodes concentrate power in terms of the number of connections they make. Google, perhaps.
A quick reading on Zipf's Law shows that many natural systems (and many artificial ones that obey similar laws of construction and equilibrium) observe 'power rules' where the distribution of power is inverse to the number of entities at any level.
Surprising that earthquakes, cities, businesses, follow the same rules. And yet quite meaningless in any direct sense because we can't manipulate these rules, only observe them.
Human social networks also follow rules that I suspect are quite simple and possibly similar to Zipf's Law. For instance, a person can only maintain a finite number of contacts (technology may increase this number but it remains finite at any given time). Any new contact coming in displaces an existing contact. So a single person's contact list will follow a power law: twice as many contacts used half as often, ten times as many contacts used a tenth as often...
Mapping a contact network would need to take the importance of each contact into account. I may have my grandmother in my list, but I speak to her once a year. My accountant - every week. My wife - twice a day. My girlfriend - every hour.
Next: the differences between individuals in terms of how much time/skill they invest in networking. Gender differences... women do this much more and better than men, in general. Age differences... younger men do it less well than older men. Wealth differences... richer people do more networking, I'd suspect, until a certain point when they start to delegate it. Very poor people do very little networking.
So, the network is not a flat map. It's got two dimensions for the lines, but each line has a thickness, and each node (individual) has a size.
Finally, I'd suspect that the network also maps power in terms of social success. Those people with the most powerful networks (a recursive definition: the networks which involve the most powerful people) will also be the most successful socially / financially.
But they may not be the happiest.