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Hagberg A, Swart PJ, Schult DA. Designing threshold networks with given structural and dynamical properties. Phys Rev E Stat Nonlin Soft Matter Phys. 2006;74(5):056116doi: 10.1103/PhysRevE.74.056116.
Hagberg, A., Swart, P. J., & Schult, D. A. (2006). Designing threshold networks with given structural and dynamical properties. Physical review. E, Statistical, nonlinear, and soft matter physics, 74(5), 056116. https://doi.org/10.1103/PhysRevE.74.056116
Hagberg, Aric, et al. "Designing threshold networks with given structural and dynamical properties." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 74,5 (2006): 056116. doi: https://doi.org/10.1103/PhysRevE.74.056116
Hagberg A, Swart PJ, Schult DA. Designing threshold networks with given structural and dynamical properties. Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Nov;74(5):056116. doi: 10.1103/PhysRevE.74.056116. Epub 2006 Nov 29. PMID: 17279977.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Nov;74(5):056116. doi: 10.1103/PhysRevE.74.056116. Epub 2006 Nov 29.

Designing threshold networks with given structural and dynamical properties.

Physical review. E, Statistical, nonlinear, and soft matter physics

Aric Hagberg, Pieter J Swart, Daniel A Schult

Affiliations

  1. Mathematical Modeling and Analysis, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.

PMID: 17279977 DOI: 10.1103/PhysRevE.74.056116

Abstract

The threshold model can be used to generate random networks of arbitrary size with given local properties such as the degree distribution, clustering, and degree correlation. We summarize the properties of networks created using the threshold model and present an alternative deterministic construction. These networks are threshold graphs and therefore contain a highly compressible layered structure and allow computation of important network properties in linear time. We show how to construct arbitrarily large, sparse, threshold networks with (approximately) any prescribed degree distribution or Laplacian spectrum. Control of the spectrum allows careful study of the synchronization properties of threshold networks including the relationship between heterogeneous degrees and resistance to synchrony.

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