On the degree evolution of a fixed vertex in some growing networks
(2011) In Statistics and Probability Letters 81(6). p.673-677- Abstract
- Two preferential attachment-type graph models which allow for dynamic addition/deletion of edges/vertices are considered. The focus of this paper is on the limiting expected degree of a fixed vertex. For both models a phase transition is seen to occur, i.e. if the probability with which edges are deleted is below a model-specific threshold value, the limiting expected degree is infinite, but if the probability is higher than the threshold value, the limiting expected degree is finite. In the regime above the critical threshold probability, however, the behaviour of the two models may differ. For one of the models a non-zero (as well as zero) limiting expected degree can be obtained whilst the other only has a zero limit. Furthermore, this... (More)
- Two preferential attachment-type graph models which allow for dynamic addition/deletion of edges/vertices are considered. The focus of this paper is on the limiting expected degree of a fixed vertex. For both models a phase transition is seen to occur, i.e. if the probability with which edges are deleted is below a model-specific threshold value, the limiting expected degree is infinite, but if the probability is higher than the threshold value, the limiting expected degree is finite. In the regime above the critical threshold probability, however, the behaviour of the two models may differ. For one of the models a non-zero (as well as zero) limiting expected degree can be obtained whilst the other only has a zero limit. Furthermore, this phase transition is seen to occur for the same critical threshold probability of removing edges as the one which determines whether the degree sequence is of power-law type or if the tails decays exponentially fast. (C) 2011 Elsevier B.V. All rights reserved. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2032533
- author
- Lindholm, Mathias and Vallier, Thomas LU
- organization
- publishing date
- 2011
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Preferential attachment, Preferential deletion, Expected degree
- in
- Statistics and Probability Letters
- volume
- 81
- issue
- 6
- pages
- 673 - 677
- publisher
- Elsevier
- external identifiers
-
- wos:000292014400008
- scopus:79952352123
- ISSN
- 0167-7152
- DOI
- 10.1016/j.spl.2011.02.015
- language
- English
- LU publication?
- yes
- id
- 0cff87ce-4b4f-4125-a979-d823f53f378d (old id 2032533)
- date added to LUP
- 2016-04-01 14:13:25
- date last changed
- 2022-01-27 23:28:52
@article{0cff87ce-4b4f-4125-a979-d823f53f378d, abstract = {{Two preferential attachment-type graph models which allow for dynamic addition/deletion of edges/vertices are considered. The focus of this paper is on the limiting expected degree of a fixed vertex. For both models a phase transition is seen to occur, i.e. if the probability with which edges are deleted is below a model-specific threshold value, the limiting expected degree is infinite, but if the probability is higher than the threshold value, the limiting expected degree is finite. In the regime above the critical threshold probability, however, the behaviour of the two models may differ. For one of the models a non-zero (as well as zero) limiting expected degree can be obtained whilst the other only has a zero limit. Furthermore, this phase transition is seen to occur for the same critical threshold probability of removing edges as the one which determines whether the degree sequence is of power-law type or if the tails decays exponentially fast. (C) 2011 Elsevier B.V. All rights reserved.}}, author = {{Lindholm, Mathias and Vallier, Thomas}}, issn = {{0167-7152}}, keywords = {{Preferential attachment; Preferential deletion; Expected degree}}, language = {{eng}}, number = {{6}}, pages = {{673--677}}, publisher = {{Elsevier}}, series = {{Statistics and Probability Letters}}, title = {{On the degree evolution of a fixed vertex in some growing networks}}, url = {{http://dx.doi.org/10.1016/j.spl.2011.02.015}}, doi = {{10.1016/j.spl.2011.02.015}}, volume = {{81}}, year = {{2011}}, }