Volume 50, Number 1, April I 2000
|Page(s)||1 - 7|
|Published online||01 September 2002|
Exactly solvable small-world network
Departamento de Física and Centro de Física do Porto, Faculdade de Ciências
Universidade do Porto -
Rua do Campo Alegre 687, 4169-007 Porto, Portugal
2 A. F. Ioffe Physico-Technical Institute - 194021 St. Petersburg, Russia
Accepted: 18 January 2000
We present an exact description of a crossover between two different regimes of simple small-world networks. Each of the sites chosen with a probability p from n sites of an ordered system defined on a circle is connected to all other sites selected in such a way. Every link is of a unit length. While p changes from 0 to 1, an averaged shortest distance between a pair of sites changes from to . We find the distribution of the shortest distances and obtain a scaling form of . In spite of the simplicity of the models under consideration, the results are close to those obtained numerically for usual small-world networks.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 64.60.Cn – Order-disorder transformations; statistical mechanics of model systems / 87.18.Sn – Neural networks
© EDP Sciences, 2000
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