Mesoscopic scales in hierarchical configuration models

Remco van der Hofstad, Johan S.H. van Leeuwaarden and Clara Stegehuis

Stochastic Processes and their Applications, 2018, vol. 128, issue 12, 4246-4276

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: Random graphs; Configuration model; Community structure; Critical behavior; Bond percolation; Brownian excursions (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spa.2018.02.006

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