A scale-free network is a connected graph or network with the property that the number of links k originating from a given node exhibits a power law distribution P(k)~k^(-γ). A scale-free network can be constructed by progressively adding nodes to an existing network and introducing links to existing nodes with preferential attachment so that the probability of linking to a given node i is proportional to the number of existing links k_i that node has, i.e., P(linking to node i)~k_i/( sum_j k_j).

connected graph | network | small world network