Random Geometric Graphs

Mathew Penrose (, Department of Mathematical Sciences, Durham University)

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English

Oxford University Press
01 June 2003

Geometry; Probability & statistics; Combinatorics & graph theory; Neural networks & fuzzy systems

Series: Oxford Studies in Probability

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 of real-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 also illustrates and extends the application to geometric probability of modern techniques including Stein's method, martingale methods and continuum percolation.

By: Mathew Penrose ( Department of Mathematical Sciences Durham University)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Volume: 5
Dimensions: Height: 241mm, Width: 162mm, Spine: 23mm
Weight: 649g
ISBN: 9780198506263
ISBN 10: 0198506260
Series: Oxford Studies in Probability
Pages: 344
Publication Date: 01 June 2003
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

1: Introduction 2: Probabilistic ingredients 3: Subgraph and component counts 4: Typical vertex degrees 5: Geometrical ingredients 6: Maximum degree, cliques and colourings 7: Minimum degree: laws of large numbers 8: Minimum degree: convergence in distribution 9: Percolative ingredients 10: Percolation and the largest component 11: The largest component for a binomial process 12: Ordering and partitioning problems 13: Connectivity and the number of components References Index

Reviews for Random Geometric Graphs

The book is suitable to design a graduate course in random geometric graphs. Its scope stretches far beyond geometric probability and includes exciting material from Poisson approximation, percolation and statistical physics. This elegantly written monograph belongs to the collection of important books vital for every probabilist. Zentralblatt MATH