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Mean-Field Solution of the Small-World Network Model

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  • M. E. J. Newman
  • C. Moore
  • D. J. Watts

Abstract

The small-world network model is a simple model of the structure of social networks, which simultaneously possesses characteristics of both regular lattices and random graphs. The model consists of a one-dimensional lattice with a low density of shortcuts added between randomly selected pairs of points. These shortcuts greatly reduce the typical path length between any two points on the lattice. We present a mean-field solution for the average path length and for the distribution of path lengths in the model. This solution is exact in the limit of large system size and either large or small number of shortcuts.

Suggested Citation

  • M. E. J. Newman & C. Moore & D. J. Watts, 1999. "Mean-Field Solution of the Small-World Network Model," Working Papers 99-09-066, Santa Fe Institute.
    • Handle: RePEc:wop:safiwp:99-09-066
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    References listed on IDEAS

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    1. A. Barrat & M. Weigt, 2000. "On the properties of small-world network models," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 13(3), pages 547-560, February.
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    Keywords

    Small worlds; social networks; mean-field theory.;
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