Emergence of the giant component in preferential-attachment growing networks

Yan Li, Yuan Sun

School of Mathematics and Physics, Shanghai University of Electric Power, Shanghai, China

Abstract: We study the percolation transition in evolving scale-free networks. A new node is added at each step and is connected to a random number of old nodes according to the preferential attachment mechanism. We give the critical value of the emergence of the giant component and prove that the transition is of infinite order. We also obtain asymptotic expressions for the cluster size distribution in the subcritical, critical, and supercritical regimes.

Keywords: scale-free network, percolation, Kosterlitz–Thouless transition, cluster size distribution.

PACS: 64.60.-i, 05.40.-a, 05.50.+q, 02.50.Cw

MSC: 05C82, 82B26, 60K35, 60J20

Received: 19.03.2015
Revised: 27.04.2015

DOI: 10.4213/tmf8939

 English version: Theoretical and Mathematical Physics, 2016, 186:3, 430–439

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