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arXiv · 1708.07739

Relaxation dynamics of maximally clustered networks

Janis Klaise·Samuel Johnson
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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 Erd\H{o}s--R\'enyi 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 Erd\H{o}s--R\'enyi phenomenology.

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Janis Klaise, Samuel Johnson. 2017-08-25. Relaxation dynamics of maximally clustered networks. https://doi.org/10.1103/physreve.97.012302

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