Journal of Applied Probability

A dynamic network in a dynamic population: asymptotic properties

Tom Britton, Mathias Lindholm, and Tatyana Turova

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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 ρ (of neighbouring nodes) which shows that ρ 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.

Article information

J. Appl. Probab., Volume 48, Number 4 (2011), 1163-1178.

First available in Project Euclid: 16 December 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 92D30: Epidemiology
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Degree correlation dynamic network phase transition random graph stationary distribution


Britton, Tom; Lindholm, Mathias; Turova, Tatyana. A dynamic network in a dynamic population: asymptotic properties. J. Appl. Probab. 48 (2011), no. 4, 1163--1178. doi:10.1239/jap/1324046025.

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