Exactly solvable small-world network
- 1 April 2000
- journal article
- Published by IOP Publishing in Europhysics Letters
- Vol. 50 (1) , 1-7
- https://doi.org/10.1209/epl/i2000-00227-1
Abstract
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 ~ n to = 1. We find the distribution of the shortest distances P(l) and obtain a scaling form of (p,n). In spite of the simplicity of the models under consideration, the results are close to those obtained numerically for usual small-world networks.Keywords
All Related Versions
This publication has 12 references indexed in Scilit:
- Spreading and shortest paths in systems with sparse long-range connectionsPhysical Review E, 1999
- Scaling and percolation in the small-world network modelPhysical Review E, 1999
- Diffusion, localization and dispersion relations on “small-world” latticesZeitschrift für Physik B Condensed Matter, 1999
- Emergence of Scaling in Random NetworksScience, 1999
- Characterization and control of small-world networksPhysical Review E, 1999
- Erratum: Small-World Networks: Evidence for a Crossover Picture [Phys. Rev. Lett. 82, 3180 (1999)]Physical Review Letters, 1999
- Small-World Networks: Evidence for a Crossover PicturePhysical Review Letters, 1999
- How to Quantify 'Small-World Networks'?Fractals, 1998
- Collective dynamics of ‘small-world’ networksNature, 1998
- It's a small worldNature, 1998