Exact results and scaling properties of small-world networks

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, ${\sigma }^2$. We also discuss the scaling properties of the distribution function. Finally, we study the limit of large system sizes and obtain some analytic results.

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

References in corpus (5)

• The diameter of the world wide web
• Mean-field theory for scale-free random networks
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• Spreading and shortest paths in systems with sparse long-range connections
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