Mean-field solution of the small-world network model

Details Mean-field solution of the small-world network model Mean-field solution of the small-world network model

1999-09-10

arxiv.org/abs/cond-mat/9909165v2

Phys. Rev. Lett. 84, 3201-3204 (2000)

Physics

Condensed Matter

Statistical Mechanics

14 pages, 2 postscript figures

Scientific paper

10.1103/PhysRevLett.84.3201

The small-world network model is a simple model of the structure of social networks, which simultaneously possesses characteristics of both regular lattices and random graphs. The model consists of a one-dimensional lattice with a low density of shortcuts added between randomly selected pairs of points. These shortcuts greatly reduce the typical path length between any two points on the lattice. We present a mean-field solution for the average path length and for the distribution of path lengths in the model. This solution is exact in the limit of large system size and either large or small number of shortcuts.

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