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This paper is concerned with statistical estimation of two preferentialattachment models: the Buckley-Osthus model and the hierarchical preferentialattachment model. We prove that the maximum likelihood estimates for bothmodels are consistent. We perform simulation studies to corroborate ourtheoretical findings. We also apply both models to study the evolution of areal-world network. A list of open problems are presented.

The Buckley-Osthus model and the block preferential attachment model: statistical analysis and application