Scale-free networks

A scale-free network is a network whose degree distribution follows a power law, at least asymptotically. That is, the fraction P(k) of nodes in the network having k connections to other nodes goes for large values of k as

$P(k)\ \sim \ ck^{\boldsymbol {-\gamma }}$

where $c$ is a normalization constant and $\gamma$ is a parameter whose value is typically in the range 2 < $\gamma$ < 3, although occasionally it may lie outside these bounds.

Scale-free networks are noteworthy because many empirically observed networks appear to be scale-free, including the World Wide Web, citation networks, biological networks, airline networks and some social networks.