Spatial preferential attachment networks:Power laws and clustering coefficients


Jacob, E. and Morters, P., 2015. Spatial preferential attachment networks:Power laws and clustering coefficients. Annals of Applied Probability, 25 (2), pp. 632-662.

Related documents:

PDF (AAP1006) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (272kB) | Preview

    Official URL:


    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.


    Item Type Articles
    CreatorsJacob, E.and Morters, P.
    DepartmentsFaculty of Science > Mathematical Sciences
    Research Centres
    Centre for Mathematical Biology
    ID Code41722


    Actions (login required)

    View Item

    Document Downloads

    More statistics for this item...