Scale-free network

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 constant and γ is a constant whose value is typically in the range 2 < γ < 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, the Internet, citation networks, and some social networks. http://en.wikipedia.org/wiki/Scale-free_network

Random vs Scale-free networks
Random network (a) and scale-free network (b). In the scale-free network, the larger hubs are highlighted.