title: Exact results and scaling properties of small-world networks
abstract: We study the distribution function for minimal paths in small-world networks. We derive its general form, which we verify numerically, and also discuss its scaling properties. Using the general form of this distribution function, we derive exact expressions for the average minimal distance &lmacr; and its variance sigma(2). Finally, we study the limit of large system sizes and obtain some approximate results.
authors.affiliation: Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA.
authors.initials: RV
authors.lastname: Kulkarni
authors.initials: E
authors.lastname: Almaas
authors.initials: D
authors.lastname: Stroud