If you happen to have checked out my presentation from University of Montana you will have read lots about my thoughts on the importance of understanding networks.
And since we’re on the topic I thought I’d point everyone to a few more network discussions of recent note.
The first comes in the most recent Forbes Magazine issue which just happens to be all about Networks. It’s actually a pretty spectacular issue (as evidenced by Chris Anderson’s envy). Anyway, the issue includes essays by some amazing folks including Metcalfe (of Metcalfe’s law fame), Murdoch, Hurley (YouTube) and DeWolfe (Myspace) — to name a few. I actually suggest buying the issue as its quite nice to have the whole thing packaged together (something you probably don’t hear that often on this site).
Anyway, the point of the issue is that networks are impossible to ignore. As more and more devices are connected, more and more networks will pop up. As more and more networks pop up, more and more power laws will emerge.
Gaussian distributions tend to prevail when events are completely independent of each other. As soon as you introduce the assumption of interdependence across events, Paretian distributions tend to surface because positive feedback loops tend to amplify small initial events. For example, the fact that a website has a lot of links increases the likelihood that others will also link to this website.
McKelvey and Andriani suggest that Gaussian distributions can morph into Paretian distributions under two conditions Ã¢â‚¬â€œ when tension increases and when the cost of connections decreases. In our globalizing economy, tension rises as competitive intensity increases and as business landscapes evolve faster than the capacity of most organizations to adapt. At the same time, costs of connections are rapidly decreasing as public policy shifts towards freer movement of goods, money and ideas and rapid improvements in the price-performance of IT infrastructures dramatically reduce the cost of information transmission. Bottom line: Paretian distributions become even more prevalent.
Power laws are a fundamental departure from how we have come to understand the world. The fact that they will only show up more often means no matter what we do, we need to understand how they work and what causes them.