Universität zu Köln

Gracar, Peter ORCID: 0000-0001-8340-8340, Grauer, Arne, Luechtrath, Lukas and Moerters, Peter (2019). The age-dependent random connection model. Queueing Syst., 93 (3-4). S. 309 - 332. DORDRECHT: SPRINGER. ISSN 1572-9443

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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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Gracar, Peter UNSPECIFIED orcid.org/0000-0001-8340-8340 UNSPECIFIED Grauer, Arne UNSPECIFIED UNSPECIFIED UNSPECIFIED Luechtrath, Lukas UNSPECIFIED UNSPECIFIED UNSPECIFIED Moerters, Peter UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-125326
DOI:	10.1007/s11134-019-09625-y
Journal or Publication Title:	Queueing Syst.
Volume:	93
Number:	3-4
Page Range:	S. 309 - 332
Date:	2019
Publisher:	SPRINGER
Place of Publication:	DORDRECHT
ISSN:	1572-9443
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language PREFERENTIAL ATTACHMENT MODEL; NETWORKS; LAWS Multiple languages Computer Science, Interdisciplinary Applications; Operations Research & Management Science Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/12532