Degree evolution in a general growing network

Umberto De Ambroggio and Hiu Ching Yip

Statistics & Probability Letters, 2024, vol. 211, issue C

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.

Keywords: Preferential attachment; Complex networks; Degree (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715224001202
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:211:y:2024:i:c:s0167715224001202

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2024.110151

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().