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.
Degree evolution in a general growing network / De Ambroggio, Umberto; Yip, HIU CHING. - In: STATISTICS & PROBABILITY LETTERS. - ISSN 0167-7152. - 211:(2024), pp. 1-6. [10.1016/j.spl.2024.110151]
Degree evolution in a general growing network
Hiu Ching, Yip
2024
Abstract
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.File | Dimensione | Formato | |
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https://hdl.handle.net/11583/2988312