Barabási-Albert model

The Barabási-Albert model is an algorithm for generating random scale-free networks by preferential attachment. It was proposed by Albert-László Barabási and Réka Albert to explain why real networks such as the Internet, the World Wide Web, citation networks and some social networks contain a few hubs with far more links than ordinary nodes. The network starts from a small set of connected nodes and grows one node at a time. Each new node links to a fixed number of existing nodes, chosen with probability proportional to the number of links those nodes already have, so well connected nodes tend to gain even more links, an effect sometimes called the rich get richer or the Matthew effect. The resulting degree distribution follows a power law, with the probability of a node having k links falling roughly as k to the power of minus three. This sets it apart from the Erdős-Rényi and Watts-Strogatz random graph models, which do not produce power laws.