LAW OF LARGE NUMBERS FOR THE LARGEST COMPONENT IN A HYPERBOLIC MODEL OF COMPLEX NETWORKS
成果类型：
Article
署名作者：
Fountoulakis, Nikolaos; Mueller, Tobias
署名单位：
University of Birmingham; Utrecht University; University of Groningen
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/17-AAP1314
发表日期：
2018
页码：
607-650
关键词：
摘要：
We consider the component structure of a recent model of random graphs on the hyperbolic plane that was introduced by Krioukov et al. The model exhibits a power law degree sequence, small distances and clustering, features that are associated with so-called complex networks. The model is controlled by two parameters alpha and nu where, roughly speaking, alpha controls the exponent of the power law and nu controls the average degree. Refining earlier results, we are able to show a law of large numbers for the largest component. That is, we show that the fraction of points in the largest component tends in probability to a constant c that depends only on alpha, nu, while all other components are sublinear. We also study how c depends on alpha, nu. To deduce our results, we introduce a local approximation of the random graph by a continuum percolation model on R-2 that may be of independent interest.