Degree evolution in a general growing network

We consider the preferential attachment model introduced by Deijfen and Lindholm (2009) in which, at every discrete time step: (i) either we add a vertex and connect it to an older vertex; or (ii) we add an edge between two random vertices; or (iii) we delete one edge. We show that, when the deletio...

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Bibliographic Details
Published in:Statistics & probability letters 2024-08, Vol.211, p.110151, Article 110151
Main Authors: De Ambroggio, Umberto, Yip, Hiu Ching
Format: Article
Language:English
Subjects:
Complex networks
Degree
Preferential attachment
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Summary:We consider the preferential attachment model introduced by Deijfen and Lindholm (2009) in which, at every discrete time step: (i) either we add a vertex and connect it to an older vertex; or (ii) we add an edge between two random vertices; or (iii) we delete one edge. We show that, when the deletion probability equals 1/3, the expected degree of any given vertex grows logarithmically, thus correcting a statement made in Lindholm and Vallier (2011). Moreover we show that, when the deletion probability is strictly less than 1/3, then the function which scales the expected degree of a given vertex, identified in Lindholm and Vallier (2011), also guarantees almost sure convergence for the degree process of a given vertex.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2024.110151