[PDF] Random Geometric Graphs eBook

Author : Mathew Penrose
Publisher : Oxford University Press
Page : 345 pages
File Size : 36,65 MB
Release : 2003
Category : Computers
ISBN : 0198506260

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This monograph provides and explains the mathematics behind geometric graph theory. Applications of this theory are used on the study of neural networks, spread of disease, astrophysics and spatial statistics.

Author : Mathew Penrose
Publisher : OUP Oxford
Page : 344 pages
File Size : 33,46 MB
Release : 2003-05-01
Category : Mathematics
ISBN : 0191545031

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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 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.

Author : Michael Krivelevich
Publisher : Cambridge University Press
Page : 129 pages
File Size : 10,17 MB
Release : 2016-04-25
Category : Mathematics
ISBN : 1316552942

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The theory of random graphs is a vital part of the education of any researcher entering the fascinating world of combinatorics. However, due to their diverse nature, the geometric and structural aspects of the theory often remain an obscure part of the formative study of young combinatorialists and probabilists. Moreover, the theory itself, even in its most basic forms, is often considered too advanced to be part of undergraduate curricula, and those who are interested usually learn it mostly through self-study, covering a lot of its fundamentals but little of the more recent developments. This book provides a self-contained and concise introduction to recent developments and techniques for classical problems in the theory of random graphs. Moreover, it covers geometric and topological aspects of the theory and introduces the reader to the diversity and depth of the methods that have been devised in this context.

Author : Alan Frieze
Publisher : Cambridge University Press
Page : 483 pages
File Size : 24,68 MB
Release : 2016
Category : Mathematics
ISBN : 1107118506

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The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.

Author : Rick Durrett
Publisher : Cambridge University Press
Page : 203 pages
File Size : 25,61 MB
Release : 2010-05-31
Category : Mathematics
ISBN : 1139460889

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The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.

Author : Remco van der Hofstad
Publisher : Cambridge University Press
Page : 341 pages
File Size : 12,58 MB
Release : 2017
Category : Computers
ISBN : 110717287X

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This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.

Author : Joel Spencer
Publisher : Springer Science & Business Media
Page : 167 pages
File Size : 35,43 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 3662045389

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The study of random graphs was begun in the 1960s and now has a comprehensive literature. This excellent book by one of the top researchers in the field now joins the study of random graphs (and other random discrete objects) with mathematical logic. The methodologies involve probability, discrete structures and logic, with an emphasis on discrete structures.

Author : Marc Barthelemy
Publisher : Springer
Page : 342 pages
File Size : 31,86 MB
Release : 2017-12-30
Category : Science
ISBN : 331920565X

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This book develops a morphodynamical approach of spatial networks with a particular emphasis on infrastructure networks such as streets, roads and transportation networks (subway, train). The author presents the mathematical tools needed to characterize these structures and how they evolve in time. The book discusses the most important empirical results and stylized facts, and will present the most important models of spatial networks. The target audience primarily comprises research scientists interested in this rapidly evolving and highly interdisciplinary field, but the book may also be beneficial for graduate students interested in large networks.