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Generating Random Networks and Graphs

Generating Random Networks and Graphs Author Alessia Annibale
ISBN-10 9780198709893
Release 2017-02-09
Pages 310
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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

Random Graphs and Complex Networks Author Remco van der Hofstad
ISBN-10 9781107172876
Release 2016-12-22
Pages 375
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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

Large Networks and Graph Limits Author László Lovász
ISBN-10 9780821890851
Release 2012
Pages 475
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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

Random Graph Dynamics Author Rick Durrett
ISBN-10 9781139460880
Release 2006-10-23
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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

A Survey of Statistical Network Models Author Anna Goldenberg
ISBN-10 9781601983206
Release 2010-01-29
Pages 120
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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.

Introduction to Random Graphs

Introduction to Random Graphs Author Alan Frieze
ISBN-10 9781107118508
Release 2015-10-31
Pages 496
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The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.


Networks Author Mark Newman
ISBN-10 9780192527493
Release 2018-07-19
Pages 784
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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.

Quantitative Assessment and Validation of Network Inference Methods in Bioinformatics

Quantitative Assessment and Validation of Network Inference Methods in Bioinformatics Author Benjamin Haibe-Kains
ISBN-10 9782889194780
Release 2015-04-14
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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.

Exponential Random Graph Models for Social Networks

Exponential Random Graph Models for Social Networks Author Dean Lusher
ISBN-10 9780521193566
Release 2012-11-19
Pages 336
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This book provides an account of the theoretical and methodological underpinnings of exponential random graph models (ERGMs).

Probability on Trees and Networks

Probability on Trees and Networks Author Russell Lyons
ISBN-10 9781316785331
Release 2017-01-20
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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.

Groups Graphs and Random Walks

Groups  Graphs and Random Walks Author Tullio Ceccherini-Silberstein
ISBN-10 9781316604403
Release 2017-06-30
Pages 542
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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.

Fundamentals of Brain Network Analysis

Fundamentals of Brain Network Analysis Author Alex Fornito
ISBN-10 9780124081185
Release 2016-03-04
Pages 494
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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

The Structure and Dynamics of Networks

The Structure and Dynamics of Networks Author Mark Newman
ISBN-10 9781400841356
Release 2011-10-23
Pages 592
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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.

Information Networking Networking Technologies for Broadband and Mobile Networks

Information Networking  Networking Technologies for Broadband and Mobile Networks Author Hyun-Kook Kahng
ISBN-10 9783540230342
Release 2004-08-31
Pages 1048
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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.


Linked Author Albert-laszlo Barabasi
ISBN-10 9780465038619
Release 2014-06-24
Pages 304
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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.

Think Complexity

Think Complexity Author Allen Downey
ISBN-10 9781492040156
Release 2018-07-11
Pages 200
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Complexity science uses computation to explore the physical and social sciences. In Think Complexity, you’ll use graphs, cellular automata, and agent-based models to study topics in physics, biology, and economics. Whether you’re an intermediate-level Python programmer or a student of computational modeling, you’ll delve into examples of complex systems through a series of worked examples, exercises, case studies, and easy-to-understand explanations. In this updated second edition, you will: Work with NumPy arrays and SciPy methods, including basic signal processing and Fast Fourier Transform Study abstract models of complex physical systems, including power laws, fractals and pink noise, and Turing machines Get Jupyter notebooks filled with starter code and solutions to help you re-implement and extend original experiments in complexity; and models of computation like Turmites, Turing machines, and cellular automata Explore the philosophy of science, including the nature of scientific laws, theory choice, and realism and instrumentalism Ideal as a text for a course on computational modeling in Python, Think Complexity also helps self-learners gain valuable experience with topics and ideas they might not encounter otherwise.

Complex Networks Their Applications V

Complex Networks   Their Applications V Author Hocine Cherifi
ISBN-10 9783319509013
Release 2016-12-30
Pages 833
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This book highlights cutting-edge research in the field of network science, offering scientists, researchers and graduate students a unique opportunity to catch up on the latest advances in theory and a multitude of applications. It presents the peer-reviewed proceedings of the fifth International Workshop on Complex Networks & their Applications (COMPLEX NETWORKS 2016), which took place in Milan during the last week of November 2016. The carefully selected papers are divided into 11 sections reflecting the diversity and richness of research areas in the field. More specifically, the following topics are covered: Network models; Network measures; Community structure; Network dynamics; Diffusion, epidemics and spreading processes; Resilience and control; Network visualization; Social and political networks; Networks in finance and economics; Biological and ecological networks; and Network analysis.