Random Graph Dynamics (Cambridge Series in Statistical and Probabilistic Mathematics) |  | Author: Rick Durrett
Publisher: Cambridge University Press
List Price: $65.00
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Rating:  1 reviews
Sales Rank: 235625
Media: Hardcover
Edition: 1
Pages: 222
Number Of Items: 1
Shipping Weight (lbs): 1.2
Dimensions (in): 10.3 x 7.1 x 0.7
ISBN: 0521866561
Dewey Decimal Number: 511.5
EAN: 9780521866569
ASIN: 0521866561
Publication Date: October 23, 2006
Availability: Usually ships in 24 hours
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Product 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 neighbours, 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 neighbours 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.
Book Description
This book presents a wide-ranging variety of mathematical argument to give insights into the small world model, the preferential attachment model and related random graphs. A unique feature is the focus on the dynamics of process taking place on the graphs in addition to geometric properties such as correctness and diameter.
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| Customer Reviews:
Good text for technical readers July 22, 2008
MANA
5 out of 5 found this review helpful
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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