On the properties of small-world network models
The European Physical Journal B - Condensed Matter, 13 (3):
547--560 (January 2000)DOI: 10.1007/s100510050067
Abstract
Abstract: We study the small-world networks recently introduced by Watts and Strogatz Nature 393, 440 (1998)&\#93;, using analytical as well as numerical tools. We characterize the geometrical properties resulting from the coexistence of a local structure and random long-range connections, and we examine their evolution with size and disorder strength. We show that any finite value of the disorder is able to trigger a "small-world" behaviour as soon as the initial lattice is big enough, and study the crossover between a regular lattice and a "small-world" one. These results are corroborated by the investigation of an Ising model defined on the network, showing for every finite disorder fraction a crossover from a high-temperature region dominated by the underlying one-dimensional structure to a mean-field like low-temperature region. In particular there exists a finite-temperature ferromagnetic phase transition as soon as the disorder strength is finite. 0.5cm&\#93;
