Random Graphs (Cambridge Studies in Advanced Mathematics, Series Number 73) 2nd Edition by Béla Bollobás (PDF)

Description

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.

User’s Reviews

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 Book Description This is a revised and updated version of the classic first edition. About the Author Béla Bollobás has taught at Cambridge University’s Department of Pure Maths and Mathematical Statistics for over 25 years and has been a fellow of Trinity College for 30 years. Since 1996, he has held the unique Chair of Excellence in the Department of Mathematical Sciences at the University of Memphis. Bollobás has previously written over 250 research papers in extremal and probabilistic combinatorics, functional analysis, probability theory, isoperimetric inequalities and polynomials of graphs. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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)

⭐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

⭐, and random graphs are pervasive in modern mathematics, so we really need a good book. This one is not bad, but…

⭐It’s a standard textbook, a benchmark one should go through in order to master random graphs.

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