Random Graph Dynamics / Edition 1
  • Random Graph Dynamics / Edition 1
  • Random Graph Dynamics / Edition 1

Random Graph Dynamics / Edition 1

by Rick Durrett, Richard Durrett
     
 

ISBN-10: 0521866561

ISBN-13: 9780521866569

Pub. Date: 10/23/2006

Publisher: Cambridge University Press

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

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Overview

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.

  • The treatment exposes the reader to a wide variety of topics in probability theory and mathematical techniques
  • A number of open ended problems are mentioned
  • The exposition concentrates on ideas behind proofs rather than technical details

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Product Details

ISBN-13:
9780521866569
Publisher:
Cambridge University Press
Publication date:
10/23/2006
Series:
Cambridge Series in Statistical and Probabilistic Mathematics, #20
Edition description:
1ST
Pages:
212
Product dimensions:
6.97(w) x 9.96(h) x 0.67(d)

Table of Contents

1. Overview; 2. Erdos–Renyi random graphs; 3. Fixed degree distributions; 4. Power laws; 5. Small worlds; 6. Random walks; 7. CHKNS model.

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