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Relaxation dynamics of maximally clustered networks
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Klaise, Janis and Johnson, Samuel (2018) Relaxation dynamics of maximally clustered networks. Physical Review E, 97 (1). 012302. doi:10.1103/PhysRevE.97.012302 ISSN 1539-3755.
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Official URL: http://dx.doi.org/10.1103/PhysRevE.97.012302
Abstract
We study the relaxation dynamics of fully clustered networks (maximal number of triangles) to an unclustered state under two different edge dynamics—the double-edge swap, corresponding to degree-preserving randomization of the configuration model, and single edge replacement, corresponding to full randomization of the Erdős-Rényi random graph. We derive expressions for the time evolution of the degree distribution, edge multiplicity distribution and clustering coefficient. We show that under both dynamics networks undergo a continuous phase transition in which a giant connected component is formed. We calculate the position of the phase transition analytically using the Erdős-Rényi phenomenology.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
Library of Congress Subject Headings (LCSH): | Triples, Theory of, Random graphs | |||||||||
Journal or Publication Title: | Physical Review E | |||||||||
Publisher: | American Physical Society | |||||||||
ISSN: | 1539-3755 | |||||||||
Official Date: | 3 January 2018 | |||||||||
Dates: |
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Volume: | 97 | |||||||||
Number: | 1 | |||||||||
Article Number: | 012302 | |||||||||
DOI: | 10.1103/PhysRevE.97.012302 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||
Date of first compliant deposit: | 21 February 2018 | |||||||||
Date of first compliant Open Access: | 22 February 2018 | |||||||||
RIOXX Funder/Project Grant: |
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