Download or read book Algorithmic Aspects of Graph Connectivity written by Hiroshi Nagamochi and published by Cambridge University Press. This book was released on 2019-05-16 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithmic Aspects of Graph Connectivity is the first comprehensive book on this central notion in graph and network theory, emphasizing its algorithmic aspects. Because of its wide applications in the fields of communication, transportation, and production, graph connectivity has made tremendous algorithmic progress under the influence of the theory of complexity and algorithms in modern computer science. The book contains various definitions of connectivity, including edge-connectivity and vertex-connectivity, and their ramifications, as well as related topics such as flows and cuts. The authors comprehensively discuss new concepts and algorithms that allow for quicker and more efficient computing, such as maximum adjacency ordering of vertices. Covering both basic definitions and advanced topics, this book can be used as a textbook in graduate courses in mathematical sciences, such as discrete mathematics, combinatorics, and operations research, and as a reference book for specialists in discrete mathematics and its applications.
Download or read book Fundamentals of Brain Network Analysis written by Alex Fornito and published by Academic Press. This book was released on 2016-03-04 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. - 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
Download or read book Generalized Connectivity of Graphs written by Xueliang Li and published by Springer. This book was released on 2016-06-30 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations with the Steiner tree packing problem and generalizations of connectivity. This book enables graduate students to understand and master a segment of graph theory and combinatorial optimization. Researchers in graph theory, combinatorics, combinatorial optimization, probability, computer science, discrete algorithms, complexity analysis, network design, and the information transferring models will find this book useful in their studies.
Download or read book Handbook of Graph Theory written by Jonathan L. Gross and published by CRC Press. This book was released on 2003-12-29 with total page 1200 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Graph Theory is the most comprehensive single-source guide to graph theory ever published. Best-selling authors Jonathan Gross and Jay Yellen assembled an outstanding team of experts to contribute overviews of more than 50 of the most significant topics in graph theory-including those related to algorithmic and optimization approach
Download or read book Connectivity in Graphs written by W. T. Tutte and published by . This book was released on 1966 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Graph and Network Theory written by Michael A. Henning and published by Springer Nature. This book was released on 2022-06-03 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook covers a diversity of topics in graph and network theory, both from a theoretical standpoint, and from an applied modelling point of view. Mathematica® is used to demonstrate much of the modelling aspects. Graph theory and model building tools are developed in tandem with effective techniques for solving practical problems via computer implementation. The book is designed with three primary readerships in mind. Individual syllabi or suggested sequences for study are provided for each of three student audiences: mathematics, applied mathematics/operations research, and computer science. In addition to the visual appeal of each page, the text contains an abundance of gems. Most chapters open with real-life problem descriptions which serve as motivation for the theoretical development of the subject matter. Each chapter concludes with three different sets of exercises. The first set of exercises are standard and geared toward the more mathematically inclined reader. Many of these are routine exercises, designed to test understanding of the material in the text, but some are more challenging. The second set of exercises is earmarked for the computer technologically savvy reader and offer computer exercises using Mathematica. The final set consists of larger projects aimed at equipping those readers with backgrounds in the applied sciences to apply the necessary skills learned in the chapter in the context of real-world problem solving. Additionally, each chapter offers biographical notes as well as pictures of graph theorists and mathematicians who have contributed significantly to the development of the results documented in the chapter. These notes are meant to bring the topics covered to life, allowing the reader to associate faces with some of the important discoveries and results presented. In total, approximately 100 biographical notes are presented throughout the book. The material in this book has been organized into three distinct parts, each with a different focus. The first part is devoted to topics in network optimization, with a focus on basic notions in algorithmic complexity and the computation of optimal paths, shortest spanning trees, maximum flows and minimum-cost flows in networks, as well as the solution of network location problems. The second part is devoted to a variety of classical problems in graph theory, including problems related to matchings, edge and vertex traversal, connectivity, planarity, edge and vertex coloring, and orientations of graphs. Finally, the focus in the third part is on modern areas of study in graph theory, covering graph domination, Ramsey theory, extremal graph theory, graph enumeration, and application of the probabilistic method.
Download or read book Properly Colored Connectivity of Graphs written by Xueliang Li and published by Springer. This book was released on 2018-05-14 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive survey of proper connection of graphs is discussed in this book with real world applications in computer science and network security. Beginning with a brief introduction, comprising relevant definitions and preliminary results, this book moves on to consider a variety of properties of graphs that imply bounds on the proper connection number. Detailed proofs of significant advancements toward open problems and conjectures are presented with complete references. Researchers and graduate students with an interest in graph connectivity and colorings will find this book useful as it builds upon fundamental definitions towards modern innovations, strategies, and techniques. The detailed presentation lends to use as an introduction to proper connection of graphs for new and advanced researchers, a solid book for a graduate level topics course, or as a reference for those interested in expanding and further developing research in the area.
Download or read book Introduction Totally and Partial Connectivity Indices in Neutrosophic graphs with Application in Behavioral Sciences written by Masoud Ghods and published by Infinite Study. This book was released on 2020-10-01 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: Connectivity is one of the most important concepts in graph theory. Since Neutrosophic Graphs are a branch of graphs, connectivity will be very important in this branch as well. In this paper, we will define the connectivity in Neutrosophic graphs using the strength of connectedness between each pair of its vertices. Also in this article, we define two new concepts of Partial connectivity index and totally connectivity index. We present several theorems related to these concepts and prove the theorems.
Download or read book Connectivity of Communication Networks written by Guoqiang Mao and published by Springer. This book was released on 2017-02-28 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a number of recent developments on connectivity of communication networks, ranging from connectivity of large static networks and connectivity of highly dynamic networks to connectivity of small to medium sized networks. This book also introduces some applications of connectivity studies in network optimization, in network localization, and in estimating distances between nodes. The book starts with an overview of the fundamental concepts, models, tools, and methodologies used for connectivity studies. The rest of the chapters are divided into four parts: connectivity of large static networks, connectivity of highly dynamic networks, connectivity of small to medium sized networks, and applications of connectivity studies.
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.
Download or read book Network Science written by Albert-László Barabási and published by Cambridge University Press. This book was released on 2016-07-21 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: Illustrated throughout in full colour, this pioneering text is the only book you need for an introduction to network science.
Download or read book Thirty Essays on Geometric Graph Theory written by János Pach and published by Springer Science & Business Media. This book was released on 2012-12-15 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many applications of graph theory, graphs are regarded as geometric objects drawn in the plane or in some other surface. The traditional methods of "abstract" graph theory are often incapable of providing satisfactory answers to questions arising in such applications. In the past couple of decades, many powerful new combinatorial and topological techniques have been developed to tackle these problems. Today geometric graph theory is a burgeoning field with many striking results and appealing open questions. This contributed volume contains thirty original survey and research papers on important recent developments in geometric graph theory. The contributions were thoroughly reviewed and written by excellent researchers in this field.
Download or read book Graphs and Matrices written by Ravindra B. Bapat and published by Springer. This book was released on 2014-09-19 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reorganized. Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory, it will also benefit readers in the sciences and engineering.
Download or read book Computational Ecology Graphs Networks And Agent based Modeling written by Wenjun Zhang and published by World Scientific. This book was released on 2012-05-04 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graphs, networks and agent-based modeling are the most thriving and attracting sciences used in ecology and environmental sciences. As such, this book is the first comprehensive treatment of the subject in the areas of ecology and environmental sciences.From this integrated and self-contained book, researchers, university teachers and students will be provided with an in-depth and complete insight on knowledge, methodology and recent advances of graphs, networks and agent-based-modeling in ecology and environmental sciences.Java codes and a standalone software package will be presented in the book for easy use for those not familiar with mathematical details.
Download or read book Magnetic Communications written by Erwu Liu and published by Cambridge University Press. This book was released on 2023-12-31 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete reference providing in-depth knowledge of magnetic communications. Ideal for graduates, researchers, and electrical engineers.
Download or read book Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs written by Jason J. Molitierno and published by CRC Press. This book was released on 2016-04-19 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the surface, matrix theory and graph theory seem like very different branches of mathematics. However, adjacency, Laplacian, and incidence matrices are commonly used to represent graphs, and many properties of matrices can give us useful information about the structure of graphs.Applications of Combinatorial Matrix Theory to Laplacian Matrices o
Download or read book Network Analysis written by Ulrik Brandes and published by Springer. This book was released on 2005-02-02 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: ‘Network’ is a heavily overloaded term, so that ‘network analysis’ means different things to different people. Specific forms of network analysis are used in the study of diverse structures such as the Internet, interlocking directorates, transportation systems, epidemic spreading, metabolic pathways, the Web graph, electrical circuits, project plans, and so on. There is, however, a broad methodological foundation which is quickly becoming a prerequisite for researchers and practitioners working with network models. From a computer science perspective, network analysis is applied graph theory. Unlike standard graph theory books, the content of this book is organized according to methods for specific levels of analysis (element, group, network) rather than abstract concepts like paths, matchings, or spanning subgraphs. Its topics therefore range from vertex centrality to graph clustering and the evolution of scale-free networks. In 15 coherent chapters, this monograph-like tutorial book introduces and surveys the concepts and methods that drive network analysis, and is thus the first book to do so from a methodological perspective independent of specific application areas.
