Issue |
Europhys. Lett.
Volume 50, Number 1, April I 2000
|
|
---|---|---|
Page(s) | 1 - 7 | |
Section | General | |
DOI | https://doi.org/10.1209/epl/i2000-00227-1 | |
Published online | 01 September 2002 |
Exactly solvable small-world network
1
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
Corresponding authors: sdorogov@fc.up.pt jfmendes@fc.up.pt
Received:
8
November
1999
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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