Relaxation dynamics of maximally clustered networks

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Relaxation dynamics of maximally clustered networks. / Klaise, Janis; Johnson, Samuel.

In: Physical Review E, Vol. 97, 03.01.2018.

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@article{ab52b80ebfe443458f350b6cc64cb4a5,
title = "Relaxation dynamics of maximally clustered networks",
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 randomizationof the Erd{\H o}s–R{\'e}nyi 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{\'e}nyi phenomenology.",
author = "Janis Klaise and Samuel Johnson",
year = "2018",
month = jan,
day = "3",
doi = "10.1103/PhysRevE.97.012302",
language = "English",
volume = "97",
journal = "Physical Review E",
issn = "1539-3755",
publisher = "American Physical Society (APS)",

}

RIS

TY - JOUR

T1 - Relaxation dynamics of maximally clustered networks

AU - Klaise, Janis

AU - Johnson, Samuel

PY - 2018/1/3

Y1 - 2018/1/3

N2 - 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 randomizationof 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.

AB - 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 randomizationof 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.

U2 - 10.1103/PhysRevE.97.012302

DO - 10.1103/PhysRevE.97.012302

M3 - Article

VL - 97

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

ER -