Random Graph Dynamics (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 20) - Hardcover

Durrett, Rick

Hardcover

ISBN 10: 0521866561 ISBN 13: 9780521866569

Publisher: Cambridge University Press, 2006

Synopsis

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.

About this title

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.

About the Author:

Rick Durrett is Professor of Mathematics at Cornell University. He received his Ph.D. in Operations Research from Stanford in 1976. After nine years at UCLA, he moved to Cornell, where his research turned to applications of probability to ecology and, more recently, genetics. He has written more than 150 papers, six other books, and has 33 academic descendants.

About this edition

• Publisher: Cambridge University Press
• Publication date: 2006
• ISBN 10: 0521866561
• ISBN 13: 9780521866569
• Binding: Hardcover
• Number of pages: 222