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On the Influence of the Seed Graph in the Preferential Attachment Model

Author(s): Bubeck, Sebastien; Mossel, Elchanan; Racz, Miklos Z

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Abstract: We study the influence of the seed graph in the preferential attachment model, focusing on the case of trees. We first show that the seed has no effect from a weak local limit point of view. On the other hand, we conjecture that different seeds lead to different distributions of limiting trees from a total variation point of view. We take a first step in proving this conjecture by showing that seeds with different degree profiles lead to different limiting distributions for the (appropriately normalized) maximum degree, implying that such seeds lead to different (in total variation) limiting trees.
Publication Date: 1-Jan-2015
Citation: Bubeck, Sebastien, Mossel, Elchanan, Racz, Miklos Z. (2015). On the Influence of the Seed Graph in the Preferential Attachment Model. IEEE Transactions on Network Science and Engineering, 2 (1), 30 - 39. doi:10.1109/TNSE.2015.2397592
DOI: doi:10.1109/TNSE.2015.2397592
ISSN: 2327-4697
Pages: 30 - 39
Type of Material: Journal Article
Journal/Proceeding Title: IEEE Transactions on Network Science and Engineering
Version: Author's manuscript

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