Random Graph Dynamics (Cambridge Series in Statistical and Probabilistic Mathematics) [Hardcover]

Rick Durrett (Author)

Book Description

ISBN-10: 0521866561 | ISBN-13: 978-0521866569 | Publication Date: October 23, 2006 | Edition: 1

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 about the same 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. While this literature is extensive, many of the papers are based on simulations and nonrigorous arguments. 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 of this book is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.

Editorial Reviews

Review

"A very valuable addition to the growing field of random graphs, providing a systematic coverage of these novel models."
Michael Krivelevich, Mathematical Reviews

"The book is written in a friendly, chatty style, making it easy to read; I very much like that. In summary, Random Graph Dynamics is a nice contribution to the area of random graphs and a source of valuable insights."
Malwina J. Luczak, Journal of the American Statistical Association

Book Description

The notion of six degrees of separation - that any two people on the planet can be connected by a short chain of people - inspired Strogatz and Watts to define the small world random graph, where each site is connected to close neighbors, but also has long range connections. At about the same time, it was observed in human social networks and on the internet that the number of neighbors of an individual has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers led to an explosion of research, but much was nonrigorous and relied on simulations. This book uses mathematical arguments to obtain insights into these graphs. A unique feature of this book is the interest in the dynamics of process taking place on the graphs in addition to their geometric properties, like correctness and diameter.

See all Editorial Reviews

Product Details

• Hardcover: 222 pages
• Publisher: Cambridge University Press; 1 edition (October 23, 2006)
• Language: English
• ISBN-10: 0521866561
• ISBN-13: 978-0521866569
• Product Dimensions: 10 x 7 x 1 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 3.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #1,633,456 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

10 of 10 people found the following review helpful:

3.0 out of 5 stars Good text for technical readers, July 21, 2008

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MANA "book worm" - See all my reviews

This review is from: Random Graph Dynamics (Cambridge Series in Statistical and Probabilistic Mathematics) (Hardcover)

The author presents very interesting material and I really learned a lot from reading this book. I've read a lot of texts and papers on the subject of random graphs (both technical and for the general public) and most authors do a good job in making this subject interesting and enjoyable, but often lack a rigorous presentation of the subject. In that sense Durrett's book does an excellent job in providing this missing element from other books. On the negative side, the exposition in Durrett' s book is not self-contained and the author relies too much on the notation and results from his previously published books. If you don't have those books the reading pace will be seriously hampered. Also, in trying to motivate the subject in Chapter 1, the author introduces a lot of cryptic notation and concepts that are not explained until later on. I know this is supposed to be a monograph, but at least the author should try to live up to the series mission of providing a clear presentation of the subjects. In summary, a great book if you are already familiar with the subject and are fairly mathematical sophisticated, but don't use this book as an introductory text or to get motivation on the subject.