Random Graph Dynamics

Author : Rick Durrett
Publisher : Cambridge University Press
ISBN 13 : 1139460889
Total Pages : 203 pages
Book Rating : 4.80/5 ( download)

DOWNLOAD NOW!

Download or read book Random Graph Dynamics written by Rick Durrett and published by Cambridge University Press. This book was released on 2010-05-31 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 a similar 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. 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 is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.

Author : Rick Durrett
Publisher : Cambridge University Press
ISBN 13 : 9780521866569
Total Pages : 222 pages
Book Rating : 4.61/5 ( download)

DOWNLOAD NOW!

Download or read book Random Graph Dynamics written by Rick Durrett and published by Cambridge University Press. This book was released on 2006-10-23 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Rick Durrett
Publisher : Cambridge University Press
ISBN 13 : 9781009521451
Total Pages : 0 pages
Book Rating : 4.54/5 ( download)

DOWNLOAD NOW!

Download or read book Dynamics on Graphs written by Rick Durrett and published by Cambridge University Press. This book was released on 2024-10-31 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This extensive revision of the 2007 book 'Random Graph Dynamics,' covering the current state of mathematical research in the field, is ideal for researchers and graduate students. It considers a small number of types of graphs, primarily the configuration model and inhomogeneous random graphs. However, it investigates a wide variety of dynamics. The author describes results for the convergence to equilibrium for random walks on random graphs as well as topics that have emerged as mature research areas since the publication of the first edition, such as epidemics, the contact process, voter models, and coalescing random walk. Chapter 8 discusses a new challenging and largely uncharted direction: systems in which the graph and the states of their vertices coevolve.

Author : Remco van der Hofstad
Publisher : Cambridge University Press
ISBN 13 : 110717287X
Total Pages : 341 pages
Book Rating : 4.76/5 ( download)

DOWNLOAD NOW!

Download or read book Random Graphs and Complex Networks written by Remco van der Hofstad and published by Cambridge University Press. This book was released on 2016-12-22 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.

Author : Béla Bollobás
Publisher : Cambridge University Press
ISBN 13 : 9780521797221
Total Pages : 520 pages
Book Rating : 4.25/5 ( download)

DOWNLOAD NOW!

Download or read book Random Graphs written by Béla Bollobás and published by Cambridge University Press. This book was released on 2001-08-30 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a revised and updated version of the classic first edition.

Author : Anthony C. C. Coolen
Publisher : Oxford University Press
ISBN 13 : 0198709897
Total Pages : 325 pages
Book Rating : 4.93/5 ( download)

DOWNLOAD NOW!

Download or read book Generating Random Networks and Graphs written by Anthony C. C. Coolen and published by Oxford University Press. This book was released on 2017 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes how to correctly and efficiently generate random networks based on certain constraints. Being able to test a hypothesis against a properly specified control case is at the heart of the 'scientific method'.

Author : Duncan J. Watts
Publisher : Princeton University Press
ISBN 13 : 0691188335
Total Pages : pages
Book Rating : 4.31/5 ( download)

DOWNLOAD NOW!

Download or read book Small Worlds written by Duncan J. Watts and published by Princeton University Press. This book was released on 2018-06-05 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Maria Eulália Vares
Publisher : Springer Nature
ISBN 13 : 3030607542
Total Pages : 819 pages
Book Rating : 4.48/5 ( download)

DOWNLOAD NOW!

Download or read book In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius written by Maria Eulália Vares and published by Springer Nature. This book was released on 2021-03-25 with total page 819 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a volume in memory of Vladas Sidoravicius who passed away in 2019. Vladas has edited two volumes appeared in this series ("In and Out of Equilibrium") and is now honored by friends and colleagues with research papers reflecting Vladas' interests and contributions to probability theory.

Author : Geoffrey Grimmett
Publisher : Cambridge University Press
ISBN 13 : 1108542999
Total Pages : 279 pages
Book Rating : 4.99/5 ( download)

DOWNLOAD NOW!

Download or read book Probability on Graphs written by Geoffrey Grimmett and published by Cambridge University Press. This book was released on 2018-01-25 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.

Author : Horst Bunke
Publisher : Springer Science & Business Media
ISBN 13 : 0817645195
Total Pages : 226 pages
Book Rating : 4.99/5 ( download)

DOWNLOAD NOW!

Download or read book A Graph-Theoretic Approach to Enterprise Network Dynamics written by Horst Bunke and published by Springer Science & Business Media. This book was released on 2007-04-05 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph treats the application of numerous graph-theoretic algorithms to a comprehensive analysis of dynamic enterprise networks. Network dynamics analysis yields valuable information about network performance, efficiency, fault prediction, cost optimization, indicators and warnings. Based on many years of applied research on generic network dynamics, this work covers a number of elegant applications (including many new and experimental results) of traditional graph theory algorithms and techniques to computationally tractable network dynamics analysis to motivate network analysts, practitioners and researchers alike.