This is a new 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 an up-to-date and comprehensive account of random graph theory. The theory estimates 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.
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Editorial Reviews
Review
"An up-to-date, comprehensive account of the random graph theory, this edition of what's considered a "classic" text contians two new sections, numerous new results, and over 150 references."
Poptronics
"The book is very impressive in the wealth of information it offers. It is bound to become a reference material on random graphs."
Miklos Bona, SIGACT News
Poptronics
"The book is very impressive in the wealth of information it offers. It is bound to become a reference material on random graphs."
Miklos Bona, SIGACT News
Book Description
This is a new edition of a now classic text. The already extensive treatment given in the first edition has been heavily revised by the author, an acknowleged expert. The addition of two new sections, numerous new results and over 150 references mean that this represents an up-to-date account of random graph theory. This book 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.
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3 of 3 people found the following review helpful:
3.0 out of 5 stars
Standard reference in the subject,
By
This review is from: Random Graphs (Cambridge Studies in Advanced Mathematics) (Hardcover)
And has a lot of material, but the organization leaves much to be desired, and standard results in the field are there but very difficult to find (for example, good luck finding the proof of the classical Erdos-Renyi theorem on connectivity threshold for random graphs. The canonical proof is about half a page, while the proof you can back out of Bollobas is maybe two chapters. The configuration model (which is actually due to the author) is actually very simple and explained well in papers by N. Wormald. It is a little painful to read about in this book. Perhaps the most widely used property of random graphs is that they have the expander property (another result of Erdos). This is also carefully hidden.
It is also a little painful for me to give a less than glowing review of this, since I really like Modern Graph Theory, and random graphs are pervasive in modern mathematics, so we really need a good book. This one is not bad, but...
4 of 7 people found the following review helpful:
4.0 out of 5 stars
Written by a Master in the Field,
By PST "A Reader from Germany" (Eislingen Deutschland) - See all my reviews
This review is from: Random Graphs (Cambridge Studies in Advanced Mathematics) (Paperback)
This is the second book by Dr. Bollobas that I have read, and it is clear, that Dr. Bollobas is a master in the field.
It is amazing, how few lines he needs to motivate the subject matter completely. The gaps in the proofs were sometimes large for me, but then again, the audience he wishes to address are "research students and professional mathematicians", and I am only a hobby mathematician. The only minus point are the large number of misprints: I counted over 130 of them, and this is not counting misprints like 'some' instead of 'same', etc. This is very annoying if one uses the book for self study. (Unfortunaltely misprints seem Dr. Bollobas' problem: Also the other book I read: 'Modern Graph Theory' had more than its share)
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Inside This Book
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First Sentence:
The aim of this chapter is to present the definitions, formulae and results of probability theory we shall need in the main body of the book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
components containing cycles, component whose order, unicyclic components, alternating inequalities, canonical labelling algorithm, labelled regular graphs, random assignment problem, random graph process, random regular graphs, unlabelled graphs, rth factorial moment, connected sparsely, giant component, infected elements, monotone increasing property, clique number, random graphs, conference graphs, independence ratio, chromatic number, cubic graphs, labelled vertices, vertex classes, local lemma, independent vertices Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Local Lemma, Proof Set, Proof Suppose, Normal Approximation, Proof By Theorem, Weighted Quick-Find, Asymmetric Graphs, Central Limit Theorem, Finding Most Comparisons, Proof Denote, Therefore Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The aim of this chapter is to present the definitions, formulae and results of probability theory we shall need in the main body of the book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
components containing cycles, component whose order, unicyclic components, alternating inequalities, canonical labelling algorithm, labelled regular graphs, random assignment problem, random graph process, random regular graphs, unlabelled graphs, rth factorial moment, connected sparsely, giant component, infected elements, monotone increasing property, clique number, random graphs, conference graphs, independence ratio, chromatic number, cubic graphs, labelled vertices, vertex classes, local lemma, independent vertices Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Local Lemma, Proof Set, Proof Suppose, Normal Approximation, Proof By Theorem, Weighted Quick-Find, Asymmetric Graphs, Central Limit Theorem, Finding Most Comparisons, Proof Denote, Therefore Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 28
books:
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97
books
cite this book:
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- Random Graphs by Svante Janson on 4 pages
- Poisson Approximation (Oxford Studies in Probability) by A. D. Barbour on page 91, and Back Matter
- Small Worlds: The Dynamics of Networks between Order and Randomness (Princeton Studies in Complexity) by Duncan J. Watts on page 277, and Back Matter
- Choice and Chance by William Allen Whitworth in Back Matter
- Complex Variables by M.R. Spiegel in Back Matter
See all 28 books this book cites
- Random Graphs by Svante Janson in Back Matter (1), and Back Matter (2)
- COLT Proceedings 1990 by COLT on page 215, and page 357
- Algorithms and Models for the Web-Graph: Third International Workshop, WAW 2004, Rome, Italy, October 16, 2004. Proceedings (Lecture Notes in Computer Science) by Stefano Leonardi on page 54, and page 103
- Six Degrees: The Science of a Connected Age (Open Market Edition) by Duncan J. Watts in Back Matter (1), and Back Matter (2)
- Randomization and Approximation Techniques in Computer Science: 6th International Workshop, RANDOM 2002, Cambridge, MA, USA, September 13-15, 2002, Proceedings (Lecture Notes in Computer Science) by Jose D.P. Rolim on page 125, and page 261
See all 97 books citing this book
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