## Generating Random Networks and Graphs

**Author**: Ton Coolen,Alessia Annibale,Ekaterina Roberts

**Publisher:**Oxford University Press

**ISBN:**019101981X

**Category:**Science

**Page:**310

**View:**4327

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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.

## Random Graphs and Complex Networks

**Author**: Remco van der Hofstad

**Publisher:**Cambridge University Press

**ISBN:**110717287X

**Category:**Computers

**Page:**375

**View:**6510

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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

**Publisher:**American Mathematical Soc.

**ISBN:**0821890859

**Category:**Mathematics

**Page:**475

**View:**4100

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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.

## Random Graph Dynamics

**Author**: Rick Durrett

**Publisher:**Cambridge University Press

**ISBN:**1139460889

**Category:**Mathematics

**Page:**N.A

**View:**8791

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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.

## Introduction to Random Graphs

**Author**: Alan Frieze,Michał Karoński

**Publisher:**Cambridge University Press

**ISBN:**1107118506

**Category:**Mathematics

**Page:**496

**View:**7134

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

## 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:**6972

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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.

## Networks

**Author**: Mark Newman

**Publisher:**Oxford University Press

**ISBN:**0192527495

**Category:**Computers

**Page:**784

**View:**7406

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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.

## 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:**4385

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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.

## 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:**9010

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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.

## 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:**8543

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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:**6907

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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

## Exponential Random Graph Models for Social Networks

*Theory, Methods, and Applications*

**Author**: Dean Lusher,Johan Koskinen,Garry Robins

**Publisher:**Cambridge University Press

**ISBN:**0521193567

**Category:**Business & Economics

**Page:**336

**View:**9397

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

## Complex Graphs and Networks

**Author**: Fan R. K. Chung,Linyuan Lu

**Publisher:**American Mathematical Soc.

**ISBN:**0821836579

**Category:**Computers

**Page:**264

**View:**1703

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Through examples of large complex graphs in realistic networks, research in graph theory has been forging ahead into exciting new directions. Graph theory has emerged as a primary tool for detecting numerous hidden structures in various information networks, including Internet graphs, social networks, biological networks, or, more generally, any graph representing relations in massive data sets. How will we explain from first principles the universal and ubiquitous coherence in the structure of these realistic but complex networks? In order to analyze these large sparse graphs, we use combinatorial, probabilistic, and spectral methods, as well as new and improved tools to analyze these networks. The examples of these networks have led us to focus on new, general, and powerful ways to look at graph theory. The book, based on lectures given at the CBMS Workshop on the Combinatorics of Large Sparse Graphs, presents new perspectives in graph theory and helps to contribute to a sound scientific foundation for our understanding of discrete networks that permeate this information age.

## 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:**771

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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.

## Probability on Trees and Networks

**Author**: Russell Lyons,Yuval Peres

**Publisher:**Cambridge University Press

**ISBN:**1316785335

**Category:**Mathematics

**Page:**N.A

**View:**425

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Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.

## Mathematical Theory of Quantum Fields

**Author**: Huzihiro Araki

**Publisher:**Oxford University Press

**ISBN:**0192539116

**Category:**Science

**Page:**N.A

**View:**1850

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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.

## 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:**9732

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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.

## Social Network Analysis for Startups

*Finding Connections on the Social Web*

**Author**: Maksim Tsvetovat,Alexander Kouznetsov

**Publisher:**"O'Reilly Media, Inc."

**ISBN:**1449306462

**Category:**Computers

**Page:**190

**View:**5549

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SNA techniques are derived from sociological and social-psychological theories and take into account the whole network (or, in case of very large networks such as Twitter -- a large segment of the network). Thus, we may arrive at results that may seem counter-intuitive -- e.g. that Jusin Bieber (7.5 mil. followers) and Lady Gaga (7.2 mil. followers) have relatively little actual influence despite their celebrity status -- while a middle-of-the-road blogger with 30K followers is able to generate tweets that "go viral" and result in millions of impressions. O'Reilly's "Mining Social Media" and "Programming Collective Intelligence" books are an excellent start for people inteseted in SNA. This book builds on these books' foundations to teach a new, pragmatic, way of doing SNA. I would like to write a book that links theory ("why is this important?", "how do various concepts interact?", "how do I interpret quantitative results?") and practice -- gathering, analyzing and visualizing data using Python and other open-source tools.

## 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:**9965

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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.