Generating Random Networks And Graphs

Author : Ton Coolen
Publisher : Oxford University Press
ISBN 13 : 019101981X
Total Pages : 310 pages
Book Rating : 4.14/5 ( download)

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Download or read book Generating Random Networks and Graphs written by Ton Coolen and published by Oxford University Press. This book was released on 2017-05-26 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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

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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 : Alan Frieze
Publisher : Cambridge University Press
ISBN 13 : 1107118506
Total Pages : 483 pages
Book Rating : 4.08/5 ( download)

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Download or read book Introduction to Random Graphs written by Alan Frieze and published by Cambridge University Press. This book was released on 2016 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.

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

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

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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 : Svante Janson
Publisher : John Wiley & Sons
ISBN 13 : 1118030966
Total Pages : 350 pages
Book Rating : 4.67/5 ( download)

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Download or read book Random Graphs written by Svante Janson and published by John Wiley & Sons. This book was released on 2011-09-30 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Fan Chung
Publisher : American Mathematical Soc.
ISBN 13 : 0821836579
Total Pages : 274 pages
Book Rating : 4.76/5 ( download)

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Download or read book Complex Graphs and Networks written by Fan Chung and published by American Mathematical Soc.. This book was released on 2006 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory is a primary tool for detecting numerous hidden structures in various information networks, including Internet graphs, social networks, biological networks, or any graph representing relations in massive data sets. This book explains the universal and ubiquitous coherence in the structure of these realistic but complex networks.

Author : Matthew O. Jackson
Publisher : Princeton University Press
ISBN 13 : 9781400833993
Total Pages : 520 pages
Book Rating : 4.9X/5 ( download)

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Download or read book Social and Economic Networks written by Matthew O. Jackson and published by Princeton University Press. This book was released on 2010-11-01 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Networks of relationships help determine the careers that people choose, the jobs they obtain, the products they buy, and how they vote. The many aspects of our lives that are governed by social networks make it critical to understand how they impact behavior, which network structures are likely to emerge in a society, and why we organize ourselves as we do. In Social and Economic Networks, Matthew Jackson offers a comprehensive introduction to social and economic networks, drawing on the latest findings in economics, sociology, computer science, physics, and mathematics. He provides empirical background on networks and the regularities that they exhibit, and discusses random graph-based models and strategic models of network formation. He helps readers to understand behavior in networked societies, with a detailed analysis of learning and diffusion in networks, decision making by individuals who are influenced by their social neighbors, game theory and markets on networks, and a host of related subjects. Jackson also describes the varied statistical and modeling techniques used to analyze social networks. Each chapter includes exercises to aid students in their analysis of how networks function. This book is an indispensable resource for students and researchers in economics, mathematics, physics, sociology, and business.

Author : James Abello
Publisher : Springer
ISBN 13 : 1461500052
Total Pages : 1209 pages
Book Rating : 4.56/5 ( download)

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Download or read book Handbook of Massive Data Sets written by James Abello and published by Springer. This book was released on 2013-12-21 with total page 1209 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Bela Bollobas
Publisher : Springer Science & Business Media
ISBN 13 : 3540693955
Total Pages : 600 pages
Book Rating : 4.56/5 ( download)

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Download or read book Handbook of Large-Scale Random Networks written by Bela Bollobas and published by Springer Science & Business Media. This book was released on 2010-05-17 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the advent of digital computers more than half a century ago, - searchers working in a wide range of scienti?c disciplines have obtained an extremely powerful tool to pursue deep understanding of natural processes in physical, chemical, and biological systems. Computers pose a great ch- lenge to mathematical sciences, as the range of phenomena available for rigorous mathematical analysis has been enormously expanded, demanding the development of a new generation of mathematical tools. There is an explosive growth of new mathematical disciplines to satisfy this demand, in particular related to discrete mathematics. However, it can be argued that at large mathematics is yet to provide the essential breakthrough to meet the challenge. The required paradigm shift in our view should be compa- ble to the shift in scienti?c thinking provided by the Newtonian revolution over 300 years ago. Studies of large-scale random graphs and networks are critical for the progress, using methods of discrete mathematics, probabil- tic combinatorics, graph theory, and statistical physics. Recent advances in large scale random network studies are described in this handbook, which provides a signi?cant update and extension - yond the materials presented in the “Handbook of Graphs and Networks” published in 2003 by Wiley. The present volume puts special emphasis on large-scale networks and random processes, which deemed as crucial for - tureprogressinthe?eld. Theissuesrelatedtorandomgraphsandnetworks pose very di?cult mathematical questions.