The age-dependent random connection model
| Autor: | Lukas Lüchtrath, Peter Gracar, Peter Mörters, Arne Grauer |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
021103 operations research
05C80 (Primary) 60K35 (Secondary) Probability (math.PR) 0211 other engineering and technologies Torus Age dependent Poisson process 02 engineering and technology Management Science and Operations Research Preferential attachment Degree distribution 01 natural sciences Computer Science Applications Combinatorics 010104 statistics & probability symbols.namesake Computational Theory and Mathematics Connection model Poisson point process symbols FOS: Mathematics 0101 mathematics Cluster analysis Mathematics - Probability Mathematics |
| DOI: | 10.48550/arxiv.1810.03429 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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