Scale-Free Network

A scale-free network is a noteworthy kind of complex network because many "real-world networks" fall into this category. For purposes of this article, "real-world" refers to any of various observable phenomena that exhibit network theoretic characteristics (see e.g., social network, computer network, neural network, epidemiology).

In scale-free networks, some nodes act as "highly connected hubs" (high degree), although most nodes are of low degree. Scale-free networks' structure and dynamics are independent of the system's size N, the number of nodes the system has. In other words, a network that is scale-free will have the same properties no matter what the number of its nodes is. Their defining characteristic is that their degree distribution follows the Yule-Simon distribution — a power law relationship defined by

where the probability P(k) that a node in the network connects with k other nodes was roughly proportional to k^−γ, and this function gave a roughly good fit to their observed data. The coefficient γ may vary approximately from 2 to 3 for most real networks, however, in some cases it can also take a value between 1 and 2