Random Geometric Graphs by Mathew Penrose

Random Geometric Graphs

byMathew Penrose

Hardcover | April 27, 2004

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This monograph sets out a body of mathematical theory for finite graphs with nodes placed randomly in Euclidean space and edges added to connect points that are close to each other. As an alternative to classical random graph models, these geometric graphs are relevant to the modelling ofreal-world networks having spatial content, arising in numerous applications such as wireless communications, parallel processing, classification, epidemiology, astronomy, and the internet. Aimed at graduate students and researchers in probability, combinatorics, statistics, and theoretical computer science, it covers topics such as edge and component counts, vertex degrees, cliques, colourings, connectivity, giant component phenomena, vertex ordering and partitioning problems. It alsoillustrates and extends the application to geometric probability of modern techniques including Stein's method, martingale methods and continuum percolation.

About The Author

Mathew Penrose is in the Department of Mathematical Sciences, Durham University.
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Title:Random Geometric GraphsFormat:HardcoverDimensions:344 pages, 9.21 × 6.14 × 0.89 inPublished:April 27, 2004Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198506260

ISBN - 13:9780198506263

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Table of Contents

1. Introduction2. Probabilistic ingredients3. Subgraph and component counts4. Typical vertex degrees5. Geometrical ingredients6. Maximum degree, cliques and colourings7. Minimum degree: laws of large numbers8. Minimum degree: convergence in distribution9. Percolative ingredients10. Percolation and the largest component11. The largest component for a binomial process12. Ordering and partitioning problems13. Connectivity and the number of componentsReferencesIndex