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Exact results and scaling properties of small-world networks

R. V. Kulkarni·E. Almaas·D. Stroud
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Abstract

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, $σ^2$. 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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R. V. Kulkarni, E. Almaas, D. Stroud. 1999-08-19. Exact results and scaling properties of small-world networks. https://doi.org/10.1103/physreve.61.4268

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