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In a one-parameter generalization of the Barabási--Albert random tree the asymptotic degree distribution on the lower levels is different from that in the whole graph.

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Acta Mathematica Hungarica
Authors: Villő Csiszár, Péter Hussami, János Komlós, Tamás F. Móri, Lídia Rejtő, and Gábor Tusnády

Abstract

There is a uniquely defined random graph model with independent adjacencies in which the degree sequence is a sufficient statistic. The model was recently discovered independently by several authors. Here we join to the statistical investigation of the model, proving that if the degree sequence is in the interior of the polytope defined by the Erdős–Gallai conditions, then a unique maximum likelihood estimate exists.

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