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The age-dependent random connection model

Author

Listed:
  • Peter Gracar

    (Universität zu Köln)

  • Arne Grauer

    (Universität zu Köln)

  • Lukas Lüchtrath

    (Universität zu Köln)

  • Peter Mörters

    (Universität zu Köln)

Abstract

We investigate a class of growing graphs embedded into the d-dimensional torus where new vertices arrive according to a Poisson process in time, are randomly placed in space and connect to existing vertices with a probability depending on time, their spatial distance and their relative birth times. This simple model for a scale-free network is called the age-based spatial preferential attachment network and is based on the idea of preferential attachment with spatially induced clustering. We show that the graphs converge weakly locally to a variant of the random connection model, which we call the age-dependent random connection model. This is a natural infinite graph on a Poisson point process where points are marked by a uniformly distributed age and connected with a probability depending on their spatial distance and both ages. We use the limiting structure to investigate asymptotic degree distribution, clustering coefficients and typical edge lengths in the age-based spatial preferential attachment network.

Suggested Citation

  • Peter Gracar & Arne Grauer & Lukas Lüchtrath & Peter Mörters, 2019. "The age-dependent random connection model," Queueing Systems: Theory and Applications, Springer, vol. 93(3), pages 309-331, December.
    • Handle: RePEc:spr:queues:v:93:y:2019:i:3:d:10.1007_s11134-019-09625-y
    DOI: 10.1007/s11134-019-09625-y
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