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Phys. Rev. E 74, 056116 (2006) [10 pages]

Designing threshold networks with given structural and dynamical properties

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Aric Hagberg and Pieter J. Swart
Mathematical Modeling and Analysis, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

Daniel A. Schult
Department of Mathematics, Colgate University, Hamilton, New York 13346, USA

Received 14 July 2006; published 29 November 2006

Thethreshold model can be used to generate random networks ofarbitrary size with given local properties such as the degreedistribution, clustering, and degree correlation. We summarize the properties ofnetworks created using the threshold model and present an alternativedeterministic construction. These networks are threshold graphs and therefore containa highly compressible layered structure and allow computation of importantnetwork properties in linear time. We show how to constructarbitrarily large, sparse, threshold networks with (approximately) any prescribed degreedistribution or Laplacian spectrum. Control of the spectrum allows carefulstudy of the synchronization properties of threshold networks including therelationship between heterogeneous degrees and resistance to synchrony.

©2006 The American Physical Society

URL:	http://link.aps.org/doi/10.1103/PhysRevE.74.056116
DOI:	10.1103/PhysRevE.74.056116
PACS:	89.75.Hc; 89.75.Da; 89.75.Fb; 05.45.Xt 89.75.Hc Networks and genealogical trees 89.75.Da Systems obeying scaling laws 89.75.Fb Structures and organization in complex systems 05.45.Xt Synchronization; coupled oscillators (nonlinear dynamical systems) YEAR: 2006
KEYWORDS:	random processes, graph theory, synchronisation

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