Power Law vs. Bell Curve

Barabasi identifies a clear distinction between how networks function in reality and how we might assume they work. In real life, many things operate on the principle of a bell curve -- class grades, height and weight, annual income, and even age. The highest concentration of any statistic is in the middle. Following this pattern, it would be implied that network connections are also randomly generated and concentrated around the average. For example, Barabasi uses websites to illustrate connectivity. It would be expected that if 100 websites had an average of 25 links, a majority of those websites would fall within that 20-30 link range.

This theory is disproven, however, with the introduction of the power law. Barabasi's research shows that websites don't follow the law of averages, and neither do other networks. He acknowledges the role of connectors, or people and groups with an unusually high number of connections. These are the people that get things accomplished, and it is part of their nature to accumulate as many links as possible. These are the kinds of people that made the Kevin Bacon game possible and such a success.

The notion of the power law is unique, because most of our other behaviors fall within the bell curve. Barabasi offers the example of human height: in our world, most people fall between 5 and 6 feet, and it is rare to know many people far outside that range. This illustrates the bell curve theory beautifully. But following the power law, he says, in a world with 6 billion people, it is possible that one person among them could be 8,000 feet tall. It is difficult to grasp that idea and examine it in the context of networks, but Barabasi does a great job highlighting examples and making the point very clear.