Spatial preferential attachment networks: Power laws and clustering coefficients

Emmanuel Jacob, Peter Morters

Research output: Contribution to journalArticle

  • 19 Citations

Abstract

We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and spatial clustering gives this model a range of interesting properties. Empirical degree distributions converge to a limit law, which can be a power law with any exponent τ>2 . The average clustering coefficient of the networks converges to a positive limit. Finally, a phase transition occurs in the global clustering coefficients and empirical distribution of edge lengths when the power-law exponent crosses the critical value τ=3 . Our main tool in the proof of these results is a general weak law of large numbers in the spirit of Penrose and Yukich.
LanguageEnglish
Pages632-662
JournalAnnals of Applied Probability
Volume25
Issue number2
Early online date19 Feb 2015
DOIs
StatusPublished - 1 Mar 2015

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Preferential Attachment
Clustering Coefficient
Empirical Distribution
Power Law
Exponent
Weak law of large numbers
Converge
Spatial Clustering
Growing Networks
Limit Laws
Degree Distribution
Vertex of a graph
Critical value
Phase Transition
Range of data
Clustering
Node
Coefficients
Power law
Model

Cite this

Spatial preferential attachment networks : Power laws and clustering coefficients. / Jacob, Emmanuel; Morters, Peter.

In: Annals of Applied Probability, Vol. 25, No. 2, 01.03.2015, p. 632-662.

Research output: Contribution to journalArticle

Jacob, Emmanuel ; Morters, Peter. / Spatial preferential attachment networks : Power laws and clustering coefficients. In: Annals of Applied Probability. 2015 ; Vol. 25, No. 2. pp. 632-662
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