Exact results and scaling properties of small-world networks

Details Exact results and scaling properties of small-world networks Exact results and scaling properties of small-world networks

1999-08-16

arxiv.org/abs/cond-mat/9908216v2

Phys. Rev. E 61, 4268 (2000)

Physics

Condensed Matter

Statistical Mechanics

RevTeX, 4 pages, 5 figures included. Minor corrections and additions

Scientific paper

10.1103/PhysRevE.61.4268

We study the distribution function for minimal paths in small-world networks. Using properties of this distribution function, we derive analytic results which greatly simplify the numerical calculation of the average minimal distance, $\bar{\ell}$, and its variance, $\sigma^2$. We also discuss the scaling properties of the distribution function. Finally, we study the limit of large system sizes and obtain some analytic results.

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