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- Title
The age-dependent random connection model.
- Authors
Gracar, Peter; Grauer, Arne; Lüchtrath, Lukas; Mörters, Peter
- 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.
- Subjects
POISSON processes; POINT processes; TORIC varieties; ASYMPTOTIC distribution; BIRTH intervals
- Publication
Queueing Systems, 2019, Vol 93, Issue 3/4, p309
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-019-09625-y