Random Graph Dynamics
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Random Graph Dynamics
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Author : Rick Durrett
language : en
Publisher: Cambridge University Press
Release Date : 2010-05-31
Random Graph Dynamics written by Rick Durrett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-31 with Mathematics categories.
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.
Random Graph Dynamics
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Author : Rick Durrett
language : en
Publisher: Cambridge University Press
Release Date : 2006-10-23
Random Graph Dynamics written by Rick Durrett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-23 with Mathematics categories.
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.
Dynamics On Graphs
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Author : Rick Durrett
language : en
Publisher: Cambridge University Press
Release Date : 2024-10-31
Dynamics On Graphs written by Rick Durrett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-31 with Mathematics categories.
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.
Small Worlds
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Author : Duncan J. Watts
language : en
Publisher: Princeton University Press
Release Date : 2018-06-05
Small Worlds written by Duncan J. Watts and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-05 with Mathematics categories.
Random Graphs
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Author : Svante Janson
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-30
Random Graphs written by Svante Janson and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-30 with Mathematics categories.
A unified, modern treatment of the theory of random graphs-including recent results and techniques Since its inception in the 1960s, the theory of random graphs has evolved into a dynamic branch of discrete mathematics. Yet despite the lively activity and important applications, the last comprehensive volume on the subject is Bollobas's well-known 1985 book. Poised to stimulate research for years to come, this new work covers developments of the last decade, providing a much-needed, modern overview of this fast-growing area of combinatorics. Written by three highly respected members of the discrete mathematics community, the book incorporates many disparate results from across the literature, including results obtained by the authors and some completely new results. Current tools and techniques are also thoroughly emphasized. Clear, easily accessible presentations make Random Graphs an ideal introduction for newcomers to the field and an excellent reference for scientists interested in discrete mathematics and theoretical computer science. Special features include: * A focus on the fundamental theory as well as basic models of random graphs * A detailed description of the phase transition phenomenon * Easy-to-apply exponential inequalities for large deviation bounds * An extensive study of the problem of containing small subgraphs * Results by Bollobas and others on the chromatic number of random graphs * The result by Robinson and Wormald on the existence of Hamilton cycles in random regular graphs * A gentle introduction to the zero-one laws * Ample exercises, figures, and bibliographic references
Random Graphs
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Author : Béla Bollobás
language : en
Publisher: Cambridge University Press
Release Date : 2001-08-30
Random Graphs written by Béla Bollobás and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-08-30 with Mathematics categories.
This is a revised and updated version of the classic first edition.
The Structure And Dynamics Of Networks
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Author : Mark Newman
language : en
Publisher: Princeton University Press
Release Date : 2011-10-23
The Structure And Dynamics Of Networks written by Mark Newman and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-23 with Mathematics categories.
From the Internet to networks of friendship, disease transmission, and even terrorism, the concept--and the reality--of networks has come to pervade modern society. But what exactly is a network? What different types of networks are there? Why are they interesting, and what can they tell us? In recent years, scientists from a range of fields--including mathematics, physics, computer science, sociology, and biology--have been pursuing these questions and building a new "science of networks." This book brings together for the first time a set of seminal articles representing research from across these disciplines. It is an ideal sourcebook for the key research in this fast-growing field. The book is organized into four sections, each preceded by an editors' introduction summarizing its contents and general theme. The first section sets the stage by discussing some of the historical antecedents of contemporary research in the area. From there the book moves to the empirical side of the science of networks before turning to the foundational modeling ideas that have been the focus of much subsequent activity. The book closes by taking the reader to the cutting edge of network science--the relationship between network structure and system dynamics. From network robustness to the spread of disease, this section offers a potpourri of topics on this rapidly expanding frontier of the new science.
Multicoloured Random Graphs The Random Dynamics Program
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Author : Sam Tarzi
language : en
Publisher:
Release Date : 2015-01-01
Multicoloured Random Graphs The Random Dynamics Program written by Sam Tarzi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-01 with categories.
The Random Dynamics program is a proposal to explain the origin of all symmetries, including Lorentz and gauge invariance without appeal to any fundamental invariance of the laws of nature, and to derive the known physical laws in such a way as to be almost unavoidable. C. D. Froggatt and H. B. Nielsen proposed in their book Origin of Symmetries, that symmetries and physical laws should arise naturally from some essentially random dynamics rather than being postulated to be exact. The program's most useful assumption that can be made about the fundamental laws is taken to be that they are random and then to see how known physics like quantum mechanics and relativity follow from this. It is believed that almost any model of these regularities would appear in some limit, for example as energies become small. Almost all theories or models at the fundamental level could then explain known physics.We suggest how using the formalism and properties of random graphs might be useful in developing the theory, and point towards directions in which it can be more fully extended in future work.
Random Walks And Diffusions On Graphs And Databases
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Author : Philipp Blanchard
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-26
Random Walks And Diffusions On Graphs And Databases written by Philipp Blanchard and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-26 with Science categories.
Most networks and databases that humans have to deal with contain large, albeit finite number of units. Their structure, for maintaining functional consistency of the components, is essentially not random and calls for a precise quantitative description of relations between nodes (or data units) and all network components. This book is an introduction, for both graduate students and newcomers to the field, to the theory of graphs and random walks on such graphs. The methods based on random walks and diffusions for exploring the structure of finite connected graphs and databases are reviewed (Markov chain analysis). This provides the necessary basis for consistently discussing a number of applications such diverse as electric resistance networks, estimation of land prices, urban planning, linguistic databases, music, and gene expression regulatory networks.
Random Graphs And Complex Networks
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Author : Remco van der Hofstad
language : en
Publisher: Cambridge University Press
Release Date : 2016-12-22
Random Graphs And Complex Networks written by Remco van der Hofstad and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-22 with Computers categories.
This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.