title: Mean-field solution of the small-world network model.
abstract: The small-world network model is a simple model of the structure of social networks, which possesses characteristics of both regular lattices and random graphs. The model consists of a one-dimensional lattice with a low density of shortcuts added between randomly selected pairs of points. These shortcuts greatly reduce the typical path length between any two points on the lattice. We present a mean-field solution for the average path length and for the distribution of path lengths in the model. This solution is exact in the limit of large system size and either a large or small number of shortcuts.
authors.affiliation: Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.
authors.forename: M E
authors.initials: ME
authors.lastname: Newman
authors.forename: C
authors.initials: C
authors.lastname: Moore
authors.forename: D J
authors.initials: DJ
authors.lastname: Watts
mesh_terms: D003198:Computer Simulation; D006801:Humans; D008433:Mathematics; D008962:Models, Theoretical; D016571:Neural Networks, Computer; D012919:Social Behavior