Exact results and scaling properties of small-world networks
R. V. Kulkarni, E. Almaas, D. Stroud
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, , and its variance, σ2. 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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