Random Graph Dynamics

Random Graph Dynamics
Author: Rick Durrett
Publisher: Cambridge University Press
Total Pages: 203
Release: 2010-05-31
Genre: Mathematics
ISBN: 1139460889

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.

Introduction to Random Graphs

Introduction to Random Graphs
Author: Alan Frieze
Publisher: Cambridge University Press
Total Pages: 483
Release: 2016
Genre: Mathematics
ISBN: 1107118506

The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.

Random Graphs and Complex Networks

Random Graphs and Complex Networks
Author: Remco van der Hofstad
Publisher: Cambridge University Press
Total Pages: 341
Release: 2017
Genre: Computers
ISBN: 110717287X

This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.

Exponential Random Graph Models for Social Networks

Exponential Random Graph Models for Social Networks
Author: Dean Lusher
Publisher: Cambridge University Press
Total Pages: 361
Release: 2013
Genre: Business & Economics
ISBN: 0521193567

This book provides an account of the theoretical and methodological underpinnings of exponential random graph models (ERGMs).

Generating Random Networks and Graphs

Generating Random Networks and Graphs
Author: Anthony C. C. Coolen
Publisher: Oxford University Press
Total Pages: 325
Release: 2017
Genre: Computers
ISBN: 0198709897

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'.

Animal Social Networks

Animal Social Networks
Author: Dr. Jens Krause
Publisher: Oxford University Press, USA
Total Pages: 279
Release: 2015
Genre: Science
ISBN: 0199679053

This book demonstrates the application of network theory to the social organization of animals.

Probability on Graphs

Probability on Graphs
Author: Geoffrey Grimmett
Publisher: Cambridge University Press
Total Pages: 279
Release: 2018-01-25
Genre: Mathematics
ISBN: 1108542999

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.

Random Walks on Infinite Graphs and Groups

Random Walks on Infinite Graphs and Groups
Author: Wolfgang Woess
Publisher: Cambridge University Press
Total Pages: 350
Release: 2000-02-13
Genre: Mathematics
ISBN: 0521552923

The main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory. The author considers Markov chains whose state space is equipped with the structure of an infinite, locally finite graph, or as a particular case, of a finitely generated group. The transition probabilities are assumed to be adapted to the underlying structure in some way that must be specified precisely in each case. From the probabilistic viewpoint, the question is what impact the particular type of structure has on various aspects of the behaviour of the random walk. Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. Links with spectral theory and discrete potential theory are also discussed. This book will be essential reading for all researchers working in stochastic process and related topics.

Handbook of Massive Data Sets

Handbook of Massive Data Sets
Author: James Abello
Publisher: Springer
Total Pages: 1209
Release: 2013-12-21
Genre: Computers
ISBN: 1461500052

The proliferation of massive data sets brings with it a series of special computational challenges. This "data avalanche" arises in a wide range of scientific and commercial applications. With advances in computer and information technologies, many of these challenges are beginning to be addressed by diverse inter-disciplinary groups, that indude computer scientists, mathematicians, statisticians and engineers, working in dose cooperation with application domain experts. High profile applications indude astrophysics, bio-technology, demographics, finance, geographi cal information systems, government, medicine, telecommunications, the environment and the internet. John R. Tucker of the Board on Mathe matical Seiences has stated: "My interest in this problern (Massive Data Sets) isthat I see it as the rnost irnportant cross-cutting problern for the rnathernatical sciences in practical problern solving for the next decade, because it is so pervasive. " The Handbook of Massive Data Sets is comprised of articles writ ten by experts on selected topics that deal with some major aspect of massive data sets. It contains chapters on information retrieval both in the internet and in the traditional sense, web crawlers, massive graphs, string processing, data compression, dustering methods, wavelets, op timization, external memory algorithms and data structures, the US national duster project, high performance computing, data warehouses, data cubes, semi-structured data, data squashing, data quality, billing in the large, fraud detection, and data processing in astrophysics, air pollution, biomolecular data, earth observation and the environment.

The Random-Cluster Model

The Random-Cluster Model
Author: Geoffrey R. Grimmett
Publisher: Springer Science & Business Media
Total Pages: 392
Release: 2006-12-13
Genre: Mathematics
ISBN: 3540328912

The random-cluster model has emerged as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems. The book includes treatment of the first-order (discontinuous) phase transition.