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Random Graph Dynamics (Cambridge Series in Statistical and Probabilistic Mathematics) Paperback – May 31, 2010

ISBN-13: 978-0521150163 ISBN-10: 0521150167 Edition: 1st

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Random Graph Dynamics (Cambridge Series in Statistical and Probabilistic Mathematics) + Probability on Graphs: Random Processes on Graphs and Lattices (Institute of Mathematical Statistics Textbooks)
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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.
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Product Details

  • Series: Cambridge Series in Statistical and Probabilistic Mathematics (Book 20)
  • Paperback: 220 pages
  • Publisher: Cambridge University Press; 1 edition (May 31, 2010)
  • Language: English
  • ISBN-10: 0521150167
  • ISBN-13: 978-0521150163
  • Product Dimensions: 8.5 x 0.4 x 10 inches
  • Shipping Weight: 15.2 ounces (View shipping rates and policies)
  • Average Customer Review: 2.3 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #1,026,431 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

13 of 13 people found the following review helpful By MANA on July 21, 2008
Format: 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.
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2 of 2 people found the following review helpful By Amazon Customer on August 24, 2013
Format: Paperback Verified Purchase
This book is definitely not for the beginner who is looking to research random graphs. Part of that is of course because of the nature of the topic, but the main issue with this book is the writing style. Durrett has a habit of using multiple notations and switching between them randomly with little explanation of what any of his terms mean. It seems to be a bit of a running joke with him. It definitely makes an already complicated topic dizzyingly confusing. That being said, this book is packed with information and Durrett is well versed on the topics.
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0 of 4 people found the following review helpful By ADAMIAK BOOKS-ABAA on September 24, 2014
Format: Paperback Verified Purchase
INACCURATE DESCRITION, ARRIVED DAMAGED DUE TO JUNK JIFFY-BAG PACKING
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