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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 186, Number 3, Pages 496–507
DOI: https://doi.org/10.4213/tmf8939 (Mi tmf8939) 		 
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
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DOI: https://doi.org/10.4213/tmf8939
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.
Funding agency Grant number
National Natural Science Foundation of China 11401368
Received: 19.03.2015
Revised: 27.04.2015
English version:
Theoretical and Mathematical Physics, 2016, Volume 186, Issue 3, Pages 430–439
DOI: https://doi.org/10.1134/S0040577916030107
Bibliographic databases:
Document Type: Article
PACS: 64.60.-i, 05.40.-a, 05.50.+q, 02.50.Cw
MSC: 05C82, 82B26, 60K35, 60J20
Language: Russian
Citation: Yan Li, Yuan Sun, “Emergence of the giant component in preferential-attachment growing networks”, TMF, 186:3 (2016), 496–507; Theoret. and Math. Phys., 186:3 (2016), 430–439
Citation in format AMSBIB
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