Gracar, P orcid.org/0000-0001-8340-8340, Grauer, A, Luechtrath, L et al. (1 more author) (2019) The age-dependent random connection model. QUEUEING SYSTEMS, 93 (3-4). pp. 309-331. ISSN 0257-0130
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | Copyright © 2019, Springer Science Business Media, LLC, part of Springer Nature |
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 |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 12 Dec 2023 15:53 |
Last Modified: | 12 Dec 2023 15:53 |
Status: | Published |
Identification Number: | 10.1007/s11134-019-09625-y |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:200619 |