Hardcover. 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 theinternet. Aimed at graduate students and researchers in probability, combinatorics, statistics, and theoretical computer science, it covers topics such as edge and component counts, vertexdegrees, 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. This monograph provides and explains the probability theory of geometric graphs. Applications of the theory include communications networks, classification, spatial statistics, epidemiology, astrophysics and neural networks. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

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Bibliographic Details

Title: Random Geometric Graphs (Hardcover)
Publisher: Oxford University Press, Oxford
Publication Date: 2003
Language: English
ISBN 10: 0198506260
ISBN 13: 9780198506263
Binding: Hardcover
Condition: new

About this title

Synopsis

This monograph provides and explains the mathematics behind geometric graph theory, which studies the properties of a graph that consists of nodes placed in Euclidean space so that edges can be added to connect points that are close to one another. For example, a collection of trees scattered in a forest and the disease that is passed between them, a set of nests of animals or birds on a region and the communication between them or communication between communications stations or nerve cells. Aimed at graduate students and researchers in probability, statistics, combinatorics and graph theory including computer scientists, it covers topics such as: technical tools, edge and component counts, vertex degrees, clique and chromatic number, and connectivity. Applications of this theory are used in the study of neural networks, spread of disease, astrophysics and spatial statistics.

About the Author

Mathew Penrose is in the Department of Mathematical Sciences, Durham University.

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