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 language | English |
|---|---|
| Pages (from-to) | 4246-4276 |
| Journal | Stochastic Processes and their Applications |
| Volume | 128 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - 1 Dec 2018 |
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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 journal › Article › Academic › peer-review
TY - JOUR
T1 - Mesoscopic scales in hierarchical configuration models
AU - van der Hofstad, Remco
AU - van Leeuwaarden, Johan S.H.
AU - Stegehuis, Clara
PY - 2018/12/1
Y1 - 2018/12/1
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 N vertices are O(N2/3). 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 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
KW - Community structure
KW - Configuration model
KW - Critical behavior
KW - Random graphs
UR - http://www.scopus.com/inward/record.url?scp=85043339109&partnerID=8YFLogxK
U2 - 10.1016/j.spa.2018.02.006
DO - 10.1016/j.spa.2018.02.006
M3 - Article
AN - SCOPUS:85043339109
VL - 128
SP - 4246
EP - 4276
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
IS - 12
ER -