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Relaxation dynamics of maximally clustered networks
Janis Klaise1, Samuel Johnson2
1Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, United Kingdom.
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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