Small-world networks: Evidence for a Crossover Picture

Marc Barthélémy*, Luís A. Nunes Amaral

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Watts and Strogatz [Nature (London) 393, 440 (1998)] have recently introduced a model for disordered networks and reported that, even for very small values of the disorder ρ in the links, the network behaves as a "small world." Here, we test the hypothesis that the appearance of small-world behavior is not a phase transition but a crossover phenomenon which depends both on the network size n and on the degree of disorder ρ. We propose that the average distance (between any two vertices of the network is a scaling function of n/n*. The crossover size n* above which the network behaves as a small world is shown to scale as n*(ρ «K 1) - ρ~T with T ≈ 2/3.

Original languageEnglish (US)
Title of host publicationThe Structure and Dynamics of Networks
PublisherPrinceton University Press
Pages304-307
Number of pages4
Volume9781400841356
ISBN (Electronic)9781400841356
ISBN (Print)0691113572, 9780691113579
StatePublished - Oct 23 2011

ASJC Scopus subject areas

  • Mathematics(all)

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