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Author: Anthony C. C. Coolen
Publisher: Oxford University Press
Published: 2017
Total Pages: 325
ISBN-13: 0198709897
DOWNLOAD EBOOKThis 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: Remco van der Hofstad
Publisher: Cambridge University Press
Published: 2017
Total Pages: 341
ISBN-13: 110717287X
DOWNLOAD EBOOKThis 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
Published: 2016
Total Pages: 483
ISBN-13: 1107118506
DOWNLOAD EBOOKThe text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.
Author: Rick Durrett
Publisher: Cambridge University Press
Published: 2010-05-31
Total Pages: 203
ISBN-13: 1139460889
DOWNLOAD EBOOKThe 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: Deepayan Chakrabarti
Publisher: Morgan & Claypool Publishers
Published: 2012-10-01
Total Pages: 209
ISBN-13: 160845116X
DOWNLOAD EBOOKWhat does the Web look like? How can we find patterns, communities, outliers, in a social network? Which are the most central nodes in a network? These are the questions that motivate this work. Networks and graphs appear in many diverse settings, for example in social networks, computer-communication networks (intrusion detection, traffic management), protein-protein interaction networks in biology, document-text bipartite graphs in text retrieval, person-account graphs in financial fraud detection, and others. In this work, first we list several surprising patterns that real graphs tend to follow. Then we give a detailed list of generators that try to mirror these patterns. Generators are important, because they can help with "what if" scenarios, extrapolations, and anonymization. Then we provide a list of powerful tools for graph analysis, and specifically spectral methods (Singular Value Decomposition (SVD)), tensors, and case studies like the famous "pageRank" algorithm and the "HITS" algorithm for ranking web search results. Finally, we conclude with a survey of tools and observations from related fields like sociology, which provide complementary viewpoints. Table of Contents: Introduction / Patterns in Static Graphs / Patterns in Evolving Graphs / Patterns in Weighted Graphs / Discussion: The Structure of Specific Graphs / Discussion: Power Laws and Deviations / Summary of Patterns / Graph Generators / Preferential Attachment and Variants / Incorporating Geographical Information / The RMat / Graph Generation by Kronecker Multiplication / Summary and Practitioner's Guide / SVD, Random Walks, and Tensors / Tensors / Community Detection / Influence/Virus Propagation and Immunization / Case Studies / Social Networks / Other Related Work / Conclusions
Author: William L. William L. Hamilton
Publisher: Springer Nature
Published: 2022-06-01
Total Pages: 141
ISBN-13: 3031015886
DOWNLOAD EBOOKGraph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.
Author: James Abello
Publisher: Springer
Published: 2013-12-21
Total Pages: 1209
ISBN-13: 1461500052
DOWNLOAD EBOOKThe 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: Dean Lusher
Publisher: Cambridge University Press
Published: 2013
Total Pages: 361
ISBN-13: 0521193567
DOWNLOAD EBOOKThis book provides an account of the theoretical and methodological underpinnings of exponential random graph models (ERGMs).
Author: Alex Fornito
Publisher: Academic Press
Published: 2016-03-04
Total Pages: 496
ISBN-13: 0124081185
DOWNLOAD EBOOKFundamentals 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. - Winner of the 2017 PROSE Award in Biomedicine & Neuroscience and the 2017 British Medical Association (BMA) Award in Neurology - 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
Author: Matthew O. Jackson
Publisher: Princeton University Press
Published: 2010-11-01
Total Pages: 519
ISBN-13: 140083399X
DOWNLOAD EBOOKNetworks 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.
