Small-world networks: Evidence for a crossover picture

Marc Barthélémy, Luis A. Nunes Amaral

Research output: Contribution to journalArticlepeer-review

238 Scopus citations

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 p 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 p. 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*(p ≪ 1)˜p with τ≈2/3.

Original languageEnglish (US)
Pages (from-to)3180-3183
Number of pages4
JournalPhysical review letters
Volume82
Issue number15
DOIs
StatePublished - 1999

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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