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

Abstract

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
Volume90
Issue number6
DOIs
StatePublished - Dec 1 2014

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Small-world Network
formulations
Formulation
Dependent
Model
Clustering Coefficient
Alternatives
Path Length
Shortest path
Complex Networks
equivalence
Intuitive
Simplify
Equivalence
Clustering
coefficients

ASJC Scopus subject areas

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

Cite this

Simple, distance-dependent formulation of the Watts-Strogatz model for directed and undirected small-world networks. / Song, H. Francis; Wang, Xiao-Jing.

In: Physical Review E, Vol. 90, No. 6, 062801, 01.12.2014.

Research output: Contribution to journalArticle

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