Random Graph Dynamics

Rick Durett - Collection Cambridge series in statistical and probabilistic mathematics

210 pages, parution le 06/02/2007

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Résumé

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

Sommaire

Overview;
Erdos-Renyi random graphs;
Fixed degree distributions;
Power laws;
Small worlds;
Random walks;
CHKNS model.

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Rick Durett
Collection	Cambridge series in statistical and probabilistic mathematics
Parution	06/02/2007
Nb. de pages	210
Format	18 x 26
Couverture	Relié
Poids	560g
Intérieur	Noir et Blanc
EAN13	9780521866569
ISBN13	978-0-521-86656-9