Spatial preferential attachment networks: Power laws and clustering coefficients

Emmanuel Jacob, Peter Morters

Research output: Contribution to journalArticle

30 Citations (Scopus)
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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.
Original languageEnglish
Pages (from-to)632-662
Number of pages31
JournalAnnals of Applied Probability
Volume25
Issue number2
Early online date19 Feb 2015
DOIs
Publication statusPublished - 31 Mar 2015

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