Random Graph Dynamics
Title | Random Graph Dynamics PDF eBook |
Author | Rick Durrett |
Publisher | Cambridge University Press |
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
Title | Introduction to Random Graphs PDF eBook |
Author | Alan Frieze |
Publisher | Cambridge University Press |
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
Title | Random Graphs and Complex Networks PDF eBook |
Author | Remco van der Hofstad |
Publisher | Cambridge University Press |
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
Title | Exponential Random Graph Models for Social Networks PDF eBook |
Author | Dean Lusher |
Publisher | Cambridge University Press |
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).
Random Graph and Growth Models
Title | Random Graph and Growth Models PDF eBook |
Author | |
Publisher | |
Pages | |
Release | 2020 |
Genre | |
ISBN | 9789179112561 |
Generating Random Networks and Graphs
Title | Generating Random Networks and Graphs PDF eBook |
Author | Anthony C. C. Coolen |
Publisher | Oxford University Press |
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'.
Large Deviations for Random Graphs
Title | Large Deviations for Random Graphs PDF eBook |
Author | Sourav Chatterjee |
Publisher | Springer |
Pages | 175 |
Release | 2017-08-31 |
Genre | Mathematics |
ISBN | 3319658166 |
This book addresses the emerging body of literature on the study of rare events in random graphs and networks. For example, what does a random graph look like if by chance it has far more triangles than expected? Until recently, probability theory offered no tools to help answer such questions. Important advances have been made in the last few years, employing tools from the newly developed theory of graph limits. This work represents the first book-length treatment of this area, while also exploring the related area of exponential random graphs. All required results from analysis, combinatorics, graph theory and classical large deviations theory are developed from scratch, making the text self-contained and doing away with the need to look up external references. Further, the book is written in a format and style that are accessible for beginning graduate students in mathematics and statistics.