The age-dependent random connection model

Peter Gracar, Arne Grauer, Lukas Lüchtrath and Peter Mörters ()
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Peter Gracar: Universität zu Köln
Arne Grauer: Universität zu Köln
Lukas Lüchtrath: Universität zu Köln
Peter Mörters: Universität zu Köln

Queueing Systems: Theory and Applications, 2019, vol. 93, issue 3, No 5, 309-331

Abstract: 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.

Keywords: Scale-free networks; Benjamini–Schramm limit; Random connection model; Preferential attachment; Geometric random graphs; Spatially embedded graphs; Clustering coefficient; Power-law degree distribution; Edge lengths; Primary 05C80; Secondary 60K35 (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11134-019-09625-y

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