Random Graph Dynamics |
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| Author:
| Durrett, Rick |
| Series title: | Cambridge Series in Statistical and Probabilistic Mathematics Ser. |
| ISBN: | 978-0-521-15016-3 |
| Publication Date: | May 2010 |
| Publisher: | Cambridge University Press
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| Book Format: | Paperback |
| List Price: | AUD $54.95 |
Book Description:
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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...
More DescriptionThe 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.