Mesoscopic scales in hierarchical configuration models

Remco van der Hofstad, Johan S. H. van Leeuwaarden, Clara Stegehuis (Corresponding Author)

Research output: Contribution to journalArticleAcademicpeer-review

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 vertices are . 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
Early online date19 Feb 2018
DOIs
Publication statusPublished - 1 Dec 2018
Externally publishedYes

Keywords

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

Cite this

van der Hofstad, Remco ; van Leeuwaarden, Johan S. H. ; Stegehuis, Clara. / Mesoscopic scales in hierarchical configuration models. In: Stochastic processes and their applications. 2018 ; Vol. 128, No. 12. pp. 4246-4276.
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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 vertices are . More specifically, the rescaled component sizes converge to the excursions of a Brownian motion with parabolic drift.",
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Mesoscopic scales in hierarchical configuration models. / van der Hofstad, Remco; van Leeuwaarden, Johan S. H.; Stegehuis, Clara (Corresponding Author).

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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AU - van der Hofstad, Remco

AU - van Leeuwaarden, Johan S. H.

AU - Stegehuis, Clara

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N2 - 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 vertices are . More specifically, the rescaled component sizes converge to the excursions of a Brownian motion with parabolic drift.

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 vertices are . More specifically, the rescaled component sizes converge to the excursions of a Brownian motion with parabolic drift.

KW - Random graphs

KW - Configuration model

KW - Community structure

KW - Critical behavior

KW - Bond percolation

KW - Brownian excursions

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