The age-dependent random connection model
Abstract
We investigate a class of growing graphs embedded into the -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 ages. 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.
Cite
@article{arxiv.1810.03429,
title = {The age-dependent random connection model},
author = {Peter Gracar and Arne Grauer and Lukas Lüchtrath and Peter Mörters},
journal= {arXiv preprint arXiv:1810.03429},
year = {2019}
}