generating random networks and graphs

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Generating Random Networks And Graphs

Author : Ton Coolen
ISBN : 9780191019814
Genre : Science
File Size : 68. 37 MB
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Generating random networks efficiently and accurately is an important challenge for practical applications, and an interesting question for theoretical study. This book presents and discusses common methods of generating random graphs. It begins with approaches such as Exponential Random Graph Models, where the targeted probability of each network appearing in the ensemble is specified. This section also includes degree-preserving randomisation algorithms, where the aim is to generate networks with the correct number of links at each node, and care must be taken to avoid introducing a bias. Separately, it looks at growth style algorithms (e.g. preferential attachment) which aim to model a real process and then to analyse the resulting ensemble of graphs. It also covers how to generate special types of graphs including modular graphs, graphs with community structure and temporal graphs. The book is aimed at the graduate student or advanced undergraduate. It includes many worked examples and open questions making it suitable for use in teaching. Explicit pseudocode algorithms are included throughout the book to make the ideas straightforward to apply. With larger and larger datasets, it is crucial to have practical and well-understood tools. Being able to test a hypothesis against a properly specified control case is at the heart of the 'scientific method'. Hence, knowledge on how to generate controlled and unbiased random graph ensembles is vital for anybody wishing to apply network science in their research.

The Generation Of Random Networks And Graphs

Author : Coolen & Roberts
ISBN : 0191780170
Genre :
File Size : 67. 12 MB
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Random Graphs And Complex Networks

Author : Remco van der Hofstad
ISBN : 9781107172876
Genre : Computers
File Size : 66. 52 MB
Format : PDF, Kindle
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This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.

Large Networks And Graph Limits

Author : László Lovász
ISBN : 9780821890851
Genre : Mathematics
File Size : 58. 76 MB
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Recently, it became apparent that a large number of the most interesting structures and phenomena of the world can be described by networks. To develop a mathematical theory of very large networks is an important challenge. This book describes one recent approach to this theory, the limit theory of graphs which has emerged over the last decade.

Gephi Cookbook

Author : Devangana Khokhar
ISBN : 9781783987412
Genre : Computers
File Size : 76. 87 MB
Format : PDF, Mobi
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If you want to learn network analysis and visualization along with graph concepts from scratch, then this book is for you. This is ideal for those of you with little or no understanding of Gephi and this domain, but will also be beneficial for those interested in expanding their knowledge and experience.

Random Graph Dynamics

Author : Rick Durrett
ISBN : 9781139460880
Genre : Mathematics
File Size : 74. 11 MB
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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.

A Survey Of Statistical Network Models

Author : Anna Goldenberg
ISBN : 9781601983206
Genre : Computers
File Size : 62. 72 MB
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"Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active "network community" and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online "networking communities" such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics."--Pages 7-8.

Introduction To Random Graphs

Author : Alan Frieze
ISBN : 9781107118508
Genre : Mathematics
File Size : 23. 80 MB
Format : PDF
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The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.


Author : Mark Newman
ISBN : 9780191500701
Genre : Science
File Size : 23. 68 MB
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The scientific study of networks, including computer networks, social networks, and biological networks, has received an enormous amount of interest in the last few years. The rise of the Internet and the wide availability of inexpensive computers have made it possible to gather and analyze network data on a large scale, and the development of a variety of new theoretical tools has allowed us to extract new knowledge from many different kinds of networks. The study of networks is broadly interdisciplinary and important developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social sciences. This book brings together for the first time the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas. Subjects covered include the measurement and structure of networks in many branches of science, methods for analyzing network data, including methods developed in physics, statistics, and sociology, the fundamentals of graph theory, computer algorithms, and spectral methods, mathematical models of networks, including random graph models and generative models, and theories of dynamical processes taking place on networks.

Exponential Random Graph Models For Social Networks

Author : Dean Lusher
ISBN : 9780521193566
Genre : Business & Economics
File Size : 30. 82 MB
Format : PDF
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This book provides an account of the theoretical and methodological underpinnings of exponential random graph models (ERGMs).

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