Networks, dynamics, and the small-world phenomenon

The small-world phenomenon formalized in this article as the coincidence of high local clustering and short global separation, is shown to be a genera l feature of sparse, decentralized networks that are neither completely ord ered nor completely random. Networks of this kind have received little atte ntion, yet they appear to be widespread in the social and natural sciences, as is indicated here by three distinct examples. Furthermore, small admixt ures of randomness to an otherwise ordered network can have a dramatic impa ct on its dynamical, as well as structural, properties-a feature illustrate d by a simple model of disease transmission.