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In this second edition of the now classic text, the already extensive treatment given in the first edition has been heavily revised by the author. The addition of two new sections, numerous new results and 150 references means that this represents a comprehensive account of random graph theory. The theory (founded by Erdos and Renyi in the late fifties) aims to estimate the number of graphs of a given degree that exhibit certain properties. It not only has numerous combinatorial applications, but also serves as a model for the probabilistic treatment of more complicated random structures. This book, written by an acknowledged expert in the field, can be used by mathematicians, computer scientists and electrical engineers, as well as people working in biomathematics. It is self-contained, and with numerous exercises in each chapter, is ideal for advanced courses or self study.
| ISBN | 0521797225 | | Weight (grammes) | 750 | | ISBN13 | 9780521797221
(What's this?) | | Published in | Cambridge | | Publisher | Cambridge University Press | | Series editor | Bollobas, B., Fulton, W., Katok, A. | | Imprint | Cambridge University Press | | Series ISSN | 73 | | Format | Paperback | | Series title | Cambridge Studies in Advanced Mathematics | | Publication date | 30 Aug 2001 | | Previous ISBN | 9780121117566 | | Library of Congress | QA166.17 .B66 2001 | | Height (mm) | 228 | | DEWEY | 511.5 | | Width (mm) | 152 | | DEWEY edition | DC21 | | Spine width (mm) | 29 | | Pages | 518 | | Academic level | Professional / Scholarly | | Volumes | 1 | |
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| | | Preface | | | | | | Notation | | | | 1 | | Probability Theoretic Preliminaries | | 1 | | 1.1 | | Notation and Basic Facts | | 1 | | 1.2 | | Some Basic Distributions | | 5 | | 1.3 | | Normal Approximation | | 9 | | 1.4 | | Inequalities | | 15 | | 1.5 | | Convergence in Distribution | | 25 | | 2 | | Models of Random Graphs | | 34 | | 2.1 | | The Basic Models | | 34 | | 2.2 | | Properties of Almost all Graphs | | 43 | | 2.3 | | Large Subsets of Vertices | | 46 | | 2.4 | | Random Regular Graphs | | 50 | | 3 | | The Degree Sequence | | 60 | | 3.1 | | The Distribution of an Element of the Degree Sequence | | 60 | | 3.2 | | Almost Determined Degrees | | 65 | | 3.3 | | The Shape of the Degree Sequence | | 69 | | 3.4 | | Jumps and Repeated Values | | 72 | | 3.5 | | Fast Algorithms for the Graph Isomorphism Problem | | 74 | | 4 | | Small Subgraphs | | 78 | | 4.1 | | Strictly Balanced Graphs | | 79 | | 4.2 | | Arbitrary Subgraphs | | 85 | | 4.3 | | Poisson Approximation | | 91 | | 5 | | The Evolution of Random Graphs - Sparse Components | | 96 | | 5.1 | | Trees of Given Sizes As Components | | 96 | | 5.2 | | The Number of Vertices on Tree Components | | 102 | | 5.3 | | The Largest Tree Components | | 110 | | | More... | | |
'... contains an enormous amount of material, assembled by one who has played a leading role in the development of the area.' Zentralblatt MATH 'This book, written by one of the leaders in the field, has become the bible of random graphs. This book is primarily for mathematicians interested in graph theory and combinatorics with probability and computing, but it could also be of interest to computer scientists. It is self-contained and lists numerous exercises in each chapter. As such, it is an excellent textbook for advanced courses or for self-study.' EMS 'There are many beautiful results in the theory of random graphs, and the main aim of the book is to introduce the reader and extensive account of a substantial body of methods and results from the theory of random graphs. This is a classic textbook suitable not only for mathematicians. It has clearly passed the test of time.' Internationale Mathematische Nachrichten '... a very good and handy guidebhook for researchers.' Acta Scientiarum Mathematicarum 'The book is very impressive in the wealth of information it offers. It is bound to become a reference material on random graphs.' SIGACT News  Be the first to write a customer review
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