On the degree evolution of a fixed vertex in some growing networks
(2011) In Statistics and Probability Letters 81(6). p.673677 Abstract
 Two preferential attachmenttype 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 modelspecific 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 nonzero (as well as zero) limiting expected degree can be obtained whilst the other only has a zero limit. Furthermore, this... (More)
 Two preferential attachmenttype 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 modelspecific 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 nonzero (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 powerlaw 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:
http://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
 01677152
 DOI
 10.1016/j.spl.2011.02.015
 language
 English
 LU publication?
 yes
 id
 0cff87ce4b4f4125a979d823f53f378d (old id 2032533)
 date added to LUP
 20110726 14:32:19
 date last changed
 20180107 07:42:56
@article{0cff87ce4b4f4125a979d823f53f378d, abstract = {Two preferential attachmenttype 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 modelspecific 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 nonzero (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 powerlaw type or if the tails decays exponentially fast. (C) 2011 Elsevier B.V. All rights reserved.}, author = {Lindholm, Mathias and Vallier, Thomas}, issn = {01677152}, keyword = {Preferential attachment,Preferential deletion,Expected degree}, language = {eng}, number = {6}, pages = {673677}, 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}, volume = {81}, year = {2011}, }