Random Geometric Graphs

TRAMA

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.

NOTE EDITORE

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.

SOMMARIO

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 components

ALTRE INFORMAZIONI

• Condizione: Nuovo
• ISBN: 9780198506263
• Collana: Oxford Studies in Probability
• Dimensioni: 241 x 22.5 x 162 mm Ø 649 gr
• Formato: Copertina rigida
• Illustration Notes: numerous figures
• Pagine Arabe: 344