Scale-free network and power law distribution. (A, B) The U.S. highway system has a bell-shaped distribution of the number of links (highway connections among cities). By contrast, the U.S. airline system has a fat tail distribution (air routes among airports). (B and C) For the bell-shaped distribution (Poisson), most nodes have comparable degrees and nodes with a large number of links absent. The average value of distribution represents the “scale” of the system. The fat tail distribution (power law) consists of numerous low degree nodes that coexist with a few highly connected hubs. The size of each node is proportional to its degree. The system does not have a mean value, and the variance becomes infinite as the system size grows, which is referred to as a “scale-free” property. In the log–log plot, the slope of power law distribution categorizes the systems and determines the behavior of scale-free networks. Modified from the original images in http://barabasi.com. Licenced under Creative Commons: CC BY-NC-SA 2.0.