Community Structure in Jazz

In the last years the physics community has devoted a strong effort to the study of social networks. The availability of large databases containing information on the collaborations between movie actors, scientists, etc. has allowed for many statistical properties of the networks to be characterized. These studies have revealed that some characteristics appear to be general for these kind of networks. In particular the average distance between any pair of vertices grows slowly, what is known as the small world property. It has also been observed that the degree distribution P(k) follows a skewed distribution. In the particular case where P(k) presents a power law tail the network is known as scale free. An interesting point which has recently raised attention is the community structure of networks. Communities appear in networks when vertices join together in tight groups that have a few connections between them. By eliminating these connections it is possible to isolate the communities. In fact this is the main idea of the algorithm that Girvan and Newman have recently proposed1.