Mesoscopic scales in hierarchical configuration models

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1 Citation (Scopus)

Abstract

To understand mesoscopic scaling in networks, we study the hierarchical configuration model (HCM), a random graph model with community structure. Connections between communities are formed as in a configuration model. We study the component sizes of HCM at criticality, and we study critical bond percolation. We find the conditions on the community sizes such that the critical component sizes of HCM behave similarly as in the configuration model. We show that the ordered components of a critical HCM on N vertices are O(N2/3). More specifically, the rescaled component sizes converge to the excursions of a Brownian motion with parabolic drift.

Original languageEnglish
Pages (from-to)4246-4276
JournalStochastic Processes and their Applications
Volume128
Issue number12
DOIs
Publication statusPublished - 1 Dec 2018

Fingerprint

Configuration
Model
Community Structure
Excursion
Graph Model
Criticality
Random Graphs
Brownian movement
Brownian motion
Scaling
Converge
Community

Keywords

  • Bond percolation
  • Brownian excursions
  • Community structure
  • Configuration model
  • Critical behavior
  • Random graphs

Cite this

@article{d47c07743a3c472fb5f2c7f53652df10,
title = "Mesoscopic scales in hierarchical configuration models",
abstract = "To understand mesoscopic scaling in networks, we study the hierarchical configuration model (HCM), a random graph model with community structure. Connections between communities are formed as in a configuration model. We study the component sizes of HCM at criticality, and we study critical bond percolation. We find the conditions on the community sizes such that the critical component sizes of HCM behave similarly as in the configuration model. We show that the ordered components of a critical HCM on N vertices are O(N2/3). More specifically, the rescaled component sizes converge to the excursions of a Brownian motion with parabolic drift.",
keywords = "Bond percolation, Brownian excursions, Community structure, Configuration model, Critical behavior, Random graphs",
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Mesoscopic scales in hierarchical configuration models. / van der Hofstad, Remco; van Leeuwaarden, Johan S.H.; Stegehuis, Clara.

In: Stochastic Processes and their Applications, Vol. 128, No. 12, 01.12.2018, p. 4246-4276.

Research output: Contribution to journalArticleAcademicpeer-review

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T1 - Mesoscopic scales in hierarchical configuration models

AU - van der Hofstad, Remco

AU - van Leeuwaarden, Johan S.H.

AU - Stegehuis, Clara

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AB - To understand mesoscopic scaling in networks, we study the hierarchical configuration model (HCM), a random graph model with community structure. Connections between communities are formed as in a configuration model. We study the component sizes of HCM at criticality, and we study critical bond percolation. We find the conditions on the community sizes such that the critical component sizes of HCM behave similarly as in the configuration model. We show that the ordered components of a critical HCM on N vertices are O(N2/3). More specifically, the rescaled component sizes converge to the excursions of a Brownian motion with parabolic drift.

KW - Bond percolation

KW - Brownian excursions

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KW - Critical behavior

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