powerlaw
While most of the systems in nature follows a bell curve, which is a distribution of that’s similar to the peaked distribution characterizing random networks. By looking at the society, we can find out that the most of the people fall in a range of height. The height of people are average out throughout the general population. (i.e. generally full-grown males fall into the range of 5-7 feet tall.) However, there are occasion in the normal bell curve distribution in different system. Instead of following bell curve, systems follow power law distribution.
Power law distribution generally describes the condition of the system where many small events coexist with a few large events. The concept of hubs existing on the web is a well-acknowledged example of power law while couple big sites work as the hub and the other web documents just scatter around. We are able to find the concept of power law distribution in the airline routing map. The big cities have enormous amount of links to almost all the other cities; however, for smaller cities, there are fewer links to other cities.
We can look at power law as an emergence from disorder to order. It is a phase transition. We look at the critical point where the system is poised to choose between 2 distinct phases. From the example of water becoming ice, we can see a clear pattern of disorder of molecules in water to perfectly ordered molecules in ice. How do power law emerge from the approach to the critical point? The molecules become clusters and other molecules join in the molecules to form the ordered pattern. We stop viewing the molecules as single elements, but to look at them as clusters. They become hubs, and other nodes (molecules) link to the hubs. It is power law at action.
The theory of phase transitions told us loud and clear that the road from disorder to order is maintained by the powerful forces of self-organization and is paved by power laws. they are patent signature of self-organization in complex systems.(Barabasi, 2001)
