A dynamic network in a dynamic population: asymptotic properties
(2011) In Journal of Applied Probability 48(4). p.1163-1178- Abstract
- We derive asymptotic properties for a stochastic dynamic network model in a stochastic dynamic population. In the model, nodes give birth to new nodes until they die, each node being equipped with a social index given at birth. During the life of a node it creates edges to other nodes, nodes with high social index at higher rate, and edges disappear randomly in time. For this model, we derive a criterion for when a giant connected component exists after the process has evolved for a long period of time, assuming that the node population grows to infinity. We also obtain an explicit expression for the degree correlation rho (of neighbouring nodes) which shows that rho is always positive irrespective of parameter values in one of the two... (More)
- We derive asymptotic properties for a stochastic dynamic network model in a stochastic dynamic population. In the model, nodes give birth to new nodes until they die, each node being equipped with a social index given at birth. During the life of a node it creates edges to other nodes, nodes with high social index at higher rate, and edges disappear randomly in time. For this model, we derive a criterion for when a giant connected component exists after the process has evolved for a long period of time, assuming that the node population grows to infinity. We also obtain an explicit expression for the degree correlation rho (of neighbouring nodes) which shows that rho is always positive irrespective of parameter values in one of the two treated submodels, and may be either positive or negative in the other model, depending on the parameters. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2348386
- author
- Britton, Tom ; Lindholm, Mathias and Turova, Tatyana LU
- organization
- publishing date
- 2011
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Degree correlation, dynamic network, phase transition, random graph, stationary distribution
- in
- Journal of Applied Probability
- volume
- 48
- issue
- 4
- pages
- 1163 - 1178
- publisher
- Applied Probability Trust
- external identifiers
-
- wos:000298938700018
- scopus:84855295964
- ISSN
- 1475-6072
- DOI
- 10.1239/jap/1324046025
- language
- English
- LU publication?
- yes
- id
- af57bf22-ea28-4d91-83e3-d320c66be048 (old id 2348386)
- date added to LUP
- 2016-04-01 09:56:06
- date last changed
- 2022-01-25 18:09:36
@article{af57bf22-ea28-4d91-83e3-d320c66be048,
abstract = {{We derive asymptotic properties for a stochastic dynamic network model in a stochastic dynamic population. In the model, nodes give birth to new nodes until they die, each node being equipped with a social index given at birth. During the life of a node it creates edges to other nodes, nodes with high social index at higher rate, and edges disappear randomly in time. For this model, we derive a criterion for when a giant connected component exists after the process has evolved for a long period of time, assuming that the node population grows to infinity. We also obtain an explicit expression for the degree correlation rho (of neighbouring nodes) which shows that rho is always positive irrespective of parameter values in one of the two treated submodels, and may be either positive or negative in the other model, depending on the parameters.}},
author = {{Britton, Tom and Lindholm, Mathias and Turova, Tatyana}},
issn = {{1475-6072}},
keywords = {{Degree correlation; dynamic network; phase transition; random graph; stationary distribution}},
language = {{eng}},
number = {{4}},
pages = {{1163--1178}},
publisher = {{Applied Probability Trust}},
series = {{Journal of Applied Probability}},
title = {{A dynamic network in a dynamic population: asymptotic properties}},
url = {{http://dx.doi.org/10.1239/jap/1324046025}},
doi = {{10.1239/jap/1324046025}},
volume = {{48}},
year = {{2011}},
}