Relaxation dynamics of maximally clustered networks

Janis Klaise and Samuel Johnson
Phys. Rev. E 97, 012302 – Published 3 January 2018

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.

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  • Received 29 August 2017

DOI:https://doi.org/10.1103/PhysRevE.97.012302

©2018 American Physical Society

Physics Subject Headings (PhySH)

NetworksInterdisciplinary Physics

Authors & Affiliations

Janis Klaise1,* and Samuel Johnson2,†

  • 1Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, United Kingdom
  • 2School of Mathematics, University of Birmingham, Birmingham B15 2TT, United Kingdom

  • *J.Klaise@warwick.ac.uk
  • s.johnson.4@bham.ac.uk

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Vol. 97, Iss. 1 — January 2018

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