Mesoscopic scales in hierarchical configuration models

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

van der Hofstad, Remco¹  van Leeuwaarden, Johan S. H.¹  Stegehuis, Clara¹ 

[1] Eindhoven Univ Technol, Dept Math & Comp Sci, POB 513, NL-5600 MB Eindhoven, Netherlands

关键词: Random graphs;    Configuration model;    Community structure;    Critical behavior;    Bond percolation;    Brownian excursions;   

DOI  :  10.1016/j.spa.2018.02.006

来源: Elsevier

【 摘 要 】

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(N-2/3). More specifically, the rescaled component sizes converge to the excursions of a Brownian motion with parabolic drift. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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