Simple, distance-dependent formulation of the Watts-Strogatz model for directed and undirected small-world networks

H. Francis Song, Xiao Jing Wang

Research output: Contribution to journalArticle


Small-world networks - complex networks characterized by a combination of high clustering and short path lengths - are widely studied using the paradigmatic model of Watts and Strogatz (WS). Although the WS model is already quite minimal and intuitive, we describe an alternative formulation of the WS model in terms of a distance-dependent probability of connection that further simplifies, both practically and theoretically, the generation of directed and undirected WS-type small-world networks. In addition to highlighting an essential feature of the WS model that has previously been overlooked, namely the equivalence to a simple distance-dependent model, this alternative formulation makes it possible to derive exact expressions for quantities such as the degree and motif distributions and global clustering coefficient for both directed and undirected networks in terms of model parameters.

Original languageEnglish (US)
Article number062801
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number6
StatePublished - Dec 1 2014


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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