Generating Random Networks and Graphs

Author: Ton Coolen,Alessia Annibale,Ekaterina Roberts

Publisher: Oxford University Press

ISBN: 019101981X

Category: Science

Page: 310

View: 6021

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.

Random Graphs and Complex Networks

Author: Remco van der Hofstad

Publisher: Cambridge University Press

ISBN: 110717287X

Category: Computers

Page: 375

View: 2928

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

Random Graph Dynamics

Author: Rick Durrett

Publisher: Cambridge University Press

ISBN: 1139460889

Category: Mathematics

Page: N.A

View: 9922

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

Author: Alan Frieze,Michał Karoński

Publisher: Cambridge University Press

ISBN: 1107118506

Category: Mathematics

Page: 496

View: 1726

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

Handbook of Graphs and Networks

From the Genome to the Internet

Author: Stefan Bornholdt,Heinz Georg Schuster

Publisher: John Wiley & Sons

ISBN: 3527606335

Category: Science

Page: 417

View: 5065

Complex interacting networks are observed in systems from such diverse areas as physics, biology, economics, ecology, and computer science. For example, economic or social interactions often organize themselves in complex network structures. Similar phenomena are observed in traffic flow and in communication networks as the internet. In current problems of the Biosciences, prominent examples are protein networks in the living cell, as well as molecular networks in the genome. On larger scales one finds networks of cells as in neural networks, up to the scale of organisms in ecological food webs. This book defines the field of complex interacting networks in its infancy and presents the dynamics of networks and their structure as a key concept across disciplines. The contributions present common underlying principles of network dynamics and their theoretical description and are of interest to specialists as well as to the non-specialized reader looking for an introduction to this new exciting field. Theoretical concepts include modeling networks as dynamical systems with numerical methods and new graph theoretical methods, but also focus on networks that change their topology as in morphogenesis and self-organization. The authors offer concepts to model network structures and dynamics, focussing on approaches applicable across disciplines.

The Structure and Dynamics of Networks

Author: Mark Newman,Albert-László Barabási,Duncan J. Watts

Publisher: Princeton University Press

ISBN: 1400841356

Category: Mathematics

Page: 592

View: 2059

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.

Gephi Cookbook

Author: Devangana Khokhar

Publisher: Packt Publishing Ltd

ISBN: 1783987413

Category: Computers

Page: 296

View: 1389

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.

A Survey of Statistical Network Models

Author: Anna Goldenberg,Alice X. Zheng,Stephen E. Fienberg,Edoardo M. Airoldi

Publisher: Now Publishers Inc

ISBN: 1601983204

Category: Computers

Page: 120

View: 9352

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.

Quantitative Assessment and Validation of Network Inference Methods in Bioinformatics

Author: Benjamin Haibe-Kains,Frank Emmert-Streib

Publisher: Frontiers Media SA

ISBN: 2889194787

Category:

Page: N.A

View: 8719

Scientists today have access to an unprecedented arsenal of high-tech tools that can be used to thoroughly characterize biological systems of interest. High-throughput “omics” technologies enable to generate enormous quantities of data at the DNA, RNA, epigenetic and proteomic levels. One of the major challenges of the post-genomic era is to extract functional information by integrating such heterogeneous high-throughput genomic data. This is not a trivial task as we are increasingly coming to understand that it is not individual genes, but rather biological pathways and networks that drive an organism’s response to environmental factors and the development of its particular phenotype. In order to fully understand the way in which these networks interact (or fail to do so) in specific states (disease for instance), we must learn both, the structure of the underlying networks and the rules that govern their behavior. In recent years there has been an increasing interest in methods that aim to infer biological networks. These methods enable the opportunity for better understanding the interactions between genomic features and the overall structure and behavior of the underlying networks. So far, such network models have been mainly used to identify and validate new interactions between genes of interest. But ultimately, one could use these networks to predict large-scale effects of perturbations, such as treatment by multiple targeted drugs. However, currently, we are still at an early stage of comprehending methods and approaches providing a robust statistical framework to quantitatively assess the quality of network inference and its predictive potential. The scope of this Research Topic in Bioinformatics and Computational Biology aims at addressing these issues by investigating the various, complementary approaches to quantify the quality of network models. These “validation” techniques could focus on assessing quality of specific interactions, global and local structures, and predictive ability of network models. These methods could rely exclusively on in silico evaluation procedures or they could be coupled with novel experimental designs to generate the biological data necessary to properly validate inferred networks.

Fundamentals of Brain Network Analysis

Author: Alex Fornito,Andrew Zalesky,Edward Bullmore

Publisher: Academic Press

ISBN: 0124081185

Category: Medical

Page: 494

View: 405

Fundamentals of Brain Network Analysis is a comprehensive and accessible introduction to methods for unraveling the extraordinary complexity of neuronal connectivity. From the perspective of graph theory and network science, this book introduces, motivates and explains techniques for modeling brain networks as graphs of nodes connected by edges, and covers a diverse array of measures for quantifying their topological and spatial organization. It builds intuition for key concepts and methods by illustrating how they can be practically applied in diverse areas of neuroscience, ranging from the analysis of synaptic networks in the nematode worm to the characterization of large-scale human brain networks constructed with magnetic resonance imaging. This text is ideally suited to neuroscientists wanting to develop expertise in the rapidly developing field of neural connectomics, and to physical and computational scientists wanting to understand how these quantitative methods can be used to understand brain organization. Extensively illustrated throughout by graphical representations of key mathematical concepts and their practical applications to analyses of nervous systems Comprehensively covers graph theoretical analyses of structural and functional brain networks, from microscopic to macroscopic scales, using examples based on a wide variety of experimental methods in neuroscience Designed to inform and empower scientists at all levels of experience, and from any specialist background, wanting to use modern methods of network science to understand the organization of the brain

Random Graphs, Geometry and Asymptotic Structure

Author: Michael Krivelevich,Konstantinos Panagiotou,Mathew Penrose,Colin McDiarmid

Publisher: Cambridge University Press

ISBN: 1316552942

Category: Mathematics

Page: N.A

View: 9932

The theory of random graphs is a vital part of the education of any researcher entering the fascinating world of combinatorics. However, due to their diverse nature, the geometric and structural aspects of the theory often remain an obscure part of the formative study of young combinatorialists and probabilists. Moreover, the theory itself, even in its most basic forms, is often considered too advanced to be part of undergraduate curricula, and those who are interested usually learn it mostly through self-study, covering a lot of its fundamentals but little of the more recent developments. This book provides a self-contained and concise introduction to recent developments and techniques for classical problems in the theory of random graphs. Moreover, it covers geometric and topological aspects of the theory and introduces the reader to the diversity and depth of the methods that have been devised in this context.

Networks

Author: Mark Newman

Publisher: Oxford University Press

ISBN: 0192527495

Category: Computers

Page: 784

View: 5435

The study of networks, including computer networks, social networks, and biological networks, has attracted enormous 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 an unprecedented scale, and the development of new theoretical tools has allowed us to extract knowledge from networks of many different kinds. The study of networks is broadly interdisciplinary and central developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social sciences. This book brings together 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. Topics covered include the measurement of networks; methods for analyzing network data, including methods developed in physics, statistics, and sociology; fundamentals of graph theory; computer algorithms; mathematical models of networks, including random graph models and generative models; and theories of dynamical processes taking place on networks.

Computational Science - ICCS 2003

International Conference, Melbourne, Australia and St. Petersburg, Russia, June 2-4, 2003. Proceedings

Author: Peter Sloot

Publisher: Springer Science & Business Media

ISBN: 3540401954

Category: Computers

Page: 1129

View: 6057

The four-volume set LNCS 2657, LNCS 2658, LNCS 2659, and LNCS 2660 constitutes the refereed proceedings of the Third International Conference on Computational Science, ICCS 2003, held concurrently in Melbourne, Australia and in St. Petersburg, Russia in June 2003. The four volumes present more than 460 reviewed contributed and invited papers and span the whole range of computational science, from foundational issues in computer science and algorithmic mathematics to advanced applications in virtually all application fields making use of computational techniques. These proceedings give a unique account of recent results in the field.

Exploratory Social Network Analysis with Pajek

Author: Wouter De Nooy,Andrej Mrvar,Vladimir Batagelj

Publisher: Cambridge University Press

ISBN: 1108474144

Category: Language Arts & Disciplines

Page: 450

View: 5356

The textbook on analysis and visualization of social networks that integrates theory, applications, and professional software for performing network analysis. Pajek software and datasets for all examples are freely available, so the reader can learn network analysis by doing it. Each chapter offers case studies for practicing network analysis.

Linked

The New Science Of Networks Science Of Networks

Author: Albert-laszlo Barabasi,Jennifer Frangos

Publisher: Basic Books

ISBN: 0465038611

Category: Science

Page: 304

View: 7431

In the 1980's, James Gleick's Chaos introduced the world to complexity. Now, Albert-László Barabási's Linked reveals the next major scientific leap: the study of networks. We've long suspected that we live in a small world, where everything is connected to everything else. Indeed, networks are pervasive--from the human brain to the Internet to the economy to our group of friends. These linkages, it turns out, aren't random. All networks, to the great surprise of scientists, have an underlying order and follow simple laws. Understanding the structure and behavior of these networks will help us do some amazing things, from designing the optimal organization of a firm to stopping a disease outbreak before it spreads catastrophically.In Linked, Barabási, a physicist whose work has revolutionized the study of networks, traces the development of this rapidly unfolding science and introduces us to the scientists carrying out this pioneering work. These "new cartographers" are mapping networks in a wide range of scientific disciplines, proving that social networks, corporations, and cells are more similar than they are different, and providing important new insights into the interconnected world around us. This knowledge, says Barabási, can shed light on the robustness of the Internet, the spread of fads and viruses, even the future of democracy. Engaging and authoritative, Linked provides an exciting preview of the next century in science, guaranteed to be transformed by these amazing discoveries.From Linked:This book has a simple message: think networks. It is about how networks emerge, what they look like, and how they evolve. It aims to develop a web-based view of nature, society, and technology, providing a unified framework to better understand issues ranging from the vulnerability of the Internet to the spread of diseases. Networks are present everywhere. All we need is an eye for them...We will see the challenges doctors face when they attempt to cure a disease by focusing on a single molecule or gene, disregarding the complex interconnected nature of the living matter. We will see that hackers are not alone in attacking networks: we all play Goliath, firing shots at a fragile ecological network that, without further support, could soon replicate our worst nightmares by turning us into an isolated group of species...Linked is meant to be an eye-opening trip that challenges you to walk across disciplines by stepping out of the box of reductionism. It is an invitation to explore link by link the next scientific revolution: the new science of networks.

Mathematical Theory of Quantum Fields

Author: Huzihiro Araki

Publisher: Oxford University Press

ISBN: 0192539116

Category: Science

Page: N.A

View: 2190

This is an introduction to the mathematical foundations of quantum field theory, using operator algebraic methods and emphasizing the link between the mathematical formulations and related physical concepts. It starts with a general probabilistic description of physics, which encompasses both classical and quantum physics. The basic key physical notions are clarified at this point. It then introduces operator algebraic methods for quantum theory, and goes on to discuss the theory of special relativity, scattering theory, and sector theory in this context.

Groups, Graphs and Random Walks

Author: Tullio Ceccherini-Silberstein,Maura Salvatori,Ecaterina Sava-Huss

Publisher: Cambridge University Press

ISBN: 1316604403

Category: Mathematics

Page: 542

View: 946

An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrdinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubtedly stem.

Six Degrees: The Science of a Connected Age

Author: Duncan J. Watts

Publisher: W. W. Norton & Company

ISBN: 0393325423

Category: Science

Page: 368

View: 4937

An architect of network theory summarizes his team's endeavor to create a blueprint of the world's networks, citing the scientific elements of the Internet, economies, terrorist organizations, and other knowledge-based groups. Reprint.

Information Networking. Networking Technologies for Broadband and Mobile Networks

International Conference ICOIN 2004, Busan, Korea, February 18-20, 2004, Revised Selected Papers

Author: Hyun-Kook Kahng,Shigeki Goto

Publisher: Springer Science & Business Media

ISBN: 3540230343

Category: Computers

Page: 1048

View: 2118

This book constitutes the thoroughly refereed post proceedings of the International Conference on Information Networking, ICOIN 2004, held in Busan, Korea, in February 2004. The 104 revised full papers presented were carefully selected during two rounds of reviewing and revision. The papers are organized in topical sections on mobile Internet and ubiquitous computing; QoS, measurement and performance analysis; high-speed network technologies; next generation Internet architecture; security; and Internet applications.