Scale-Free Network

A scale-free network is a connected graph or network with the property that the number of links  originating from a given node exhibits a power law distribution . 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  is proportional to the number of existing links  that node has, i.e.,

Scale-free networks occur in many areas of science and engineering, including the topology of web pages (where the nodes are individual web pages and the links are hyper-links), the collaborative network of Hollywood actors (where the nodes actors and the links are co-stars in the same movie), the power grid of the western United States (where the nodes are generators, transformers, and substations and the links are power transmission lines), and the peer-reviewed scientific literature (where the nodes are publications and the links are citations).

REFERENCES

Barabási, A-L. and Albert, R. "Emergence of Scaling in Random Networks." Science 286, 509-512, 1999.

Barabási, A-L.; Albert, R.; and Jeong, H. "Mean-Field Theory for Scale-Free Random Networks." Physica A 272, 173-187, 1999.