Exact results and scaling properties of small-world networks

R. V. Kulkarni, E. Almaas, and D. Stroud
Phys. Rev. E 61, 4268 – Published 1 April 2000
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Abstract

We study the distribution function for minimal paths in small-world networks. We derive its general form, which we verify numerically, and also discuss its scaling properties. Using the general form of this distribution function, we derive exact expressions for the average minimal distance l¯ and its variance σ2. Finally, we study the limit of large system sizes and obtain some approximate results.

  • Received 19 August 1999

DOI:https://doi.org/10.1103/PhysRevE.61.4268

©2000 American Physical Society

Authors & Affiliations

R. V. Kulkarni*, E. Almaas, and D. Stroud

  • Department of Physics, The Ohio State University, Columbus, Ohio 43210

  • *Electronic address: rahul@mps.ohio-state.edu

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Vol. 61, Iss. 4 — April 2000

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