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This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study. From the reviews: “This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory.”Acta Scientiarum Mathematiciarum “Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has depth and integrity. ”Persi Diaconis & Ron Graham, SIAM Review “The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theory.” Bulletin of the Institute of Combinatorics and its Applications “Succeeds dramatically ... a hell of a good ook.” MAA Reviews “A highlight of the book is what is by far the best account in print of the Seymour-Robertson theory of graph minors.” Mathematika “ ... like listening to someone explain mathematics.” Bulletin of the AMS.

Graph theory --- Graphes, Théorie des --- Grafos, Teoría de --- Combinatorics. --- Computer science. --- Math Applications in Computer Science. --- Graphes, Théorie des. --- Informatics --- Science --- Combinatorics --- Algebra --- Mathematical analysis --- Graphentheorie. --- Computer science—Mathematics. --- Discrete mathematics. --- Computer science --- Discrete Mathematics. --- Mathematical Applications in Computer Science. --- Mathematics. --- Computer mathematics --- Electronic data processing --- Mathematics --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Graphes, Théorie des.

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Algorithms, graphs, and computers

Dynamic programming. --- Algorithms. --- Graph theory. --- 519.12 --- 519.12 Permutations in general. Groups where order is taken into account --- Permutations in general. Groups where order is taken into account --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Mathematical optimization --- Programming (Mathematics) --- Systems engineering --- Algorism --- Algebra --- Arithmetic --- Extremal problems --- Foundations --- Informatique --- Computer science --- Algorithmes --- Graphes, Théorie des --- Graphes, Théorie des

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Graph theory continues to be one of the fastest growing areas of modern mathematics because of its wide applicability in such diverse disciplines as computer science, engineering, chemistry, management science, social science, and resource planning. Graphs arise as mathematical models in these fields, and the theory of graphs provides a spectrum of methods of proof. This concisely written textbook is intended for an introductory course in graph theory for undergraduate mathematics majors or advanced undergraduate and graduate students from the many fields that benefit from graph-theoretic applications. Key features: * Introductory chapters present the main ideas and topics in graph theory—walks, paths and cycles, radius, diameter, eccentricity, cuts and connectivity, trees * Subsequent chapters examine specialized topics and applications * Numerous examples and illustrations * Comprehensive index and bibliography, with suggested literature for more advanced material New to the second edition: * New chapters on labeling and on communications networks and small-worlds * Expanded beginner’s material in the early chapters, including more examples, exercises, hints and solutions to key problems * Many additional changes, improvements, and corrections throughout resulting from classroom use and feedback Striking a balance between a theoretical and practical approach with a distinctly applied flavor, this gentle introduction to graph theory consists of carefully chosen topics to develop graph-theoretic reasoning for a mixed audience. Familiarity with the basic concepts of set theory, along with some background in matrices and algebra, and a little mathematical maturity are the only prerequisites. ----- From a review of the first edition: "Altogether the book gives a comprehensive introduction to graphs, their theory and their application…The use of the text is optimized when the exercises are solved. The obtained skills improve understanding of graph theory as well… It is very useful that the solutions of these exercises are collected in an appendix." —Simulation News Europe.

Graph theory --- Combinatorial analysis --- Théorie des graphes --- Analyse combinatoire --- Algorithms. --- Electronic books. -- local. --- Graph theory. --- Mathematics --- Algebra --- Physical Sciences & Mathematics --- 519.1 --- Graphs, Theory of --- Theory of graphs --- Topology --- Combinatorics. Graph theory --- Extremal problems --- 519.1 Combinatorics. Graph theory --- Graphes, Théorie des --- Théorie des graphes --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Algorism --- Mathematics. --- Algebra. --- Matrix theory. --- Applied mathematics. --- Engineering mathematics. --- Mathematical logic. --- Discrete mathematics. --- Combinatorics. --- Discrete Mathematics. --- Applications of Mathematics. --- Mathematical Logic and Foundations. --- Linear and Multilinear Algebras, Matrix Theory. --- Arithmetic --- Foundations --- Logic, Symbolic and mathematical. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Math --- Science --- Combinatorics --- Mathematical analysis --- Graphes, Théorie des. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Engineering --- Engineering analysis --- Théorie des graphes.

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In the past decade, the study of networks has increased dramatically. Researchers from across the sciences—including biology and bioinformatics, computer science, economics, engineering, mathematics, physics, sociology, and statistics—are more and more involved with the collection and statistical analysis of network-indexed data. As a result, statistical methods and models are being developed in this area at a furious pace, with contributions coming from a wide spectrum of disciplines. This book provides an up-to-date treatment of the foundations common to the statistical analysis of network data across the disciplines. The material is organized according to a statistical taxonomy, although the presentation entails a conscious balance of concepts versus mathematics. In addition, the examples—including extended cases studies—are drawn widely from the literature. This book should be of substantial interest both to statisticians and to anyone else working in the area of ‘network science.’ The coverage of topics in this book is broad, but unfolds in a systematic manner, moving from descriptive (or exploratory) methods, to sampling, to modeling and inference. Specific topics include network mapping, characterization of network structure, network sampling, and the modeling, inference, and prediction of networks, network processes, and network flows. This book is the first such resource to present material on all of these core topics in one place. Eric Kolaczyk is a professor of statistics, and Director of the Program in Statistics, in the Department of Mathematics and Statistics at Boston University, where he also is an affiliated faculty member in the Center for Biodynamics, the Program in Bioinformatics, and the Division of Systems Engineering. His publications on network-based topics include work ranging from the detection of anomalous traffic patterns in computer networks to the prediction of biological function in networks of interacting proteins to the characterization of influence of groups of actors in social networks.

methodologieën --- informatica --- database management --- statistisch onderzoek --- sociale wetenschappen --- bio-informatica --- Mathematical statistics --- communicatietechnologie --- System analysis --- Analyse de systèmes --- Statistical methods. --- Méthodes statistiques. --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Statistical methods --- Computer Communication Networks. --- Distribution (Probability theory. --- Mathematical statistics. --- Data mining. --- Bioinformatics. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Complex Systems. --- Data Mining and Knowledge Discovery. --- Bio-informatics --- Biological informatics --- Biology --- Information science --- Computational biology --- Systems biology --- Algorithmic knowledge discovery --- Factual data analysis --- KDD (Information retrieval) --- Knowledge discovery in data --- Knowledge discovery in databases --- Mining, Data --- Database searching --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Distribution functions --- Frequency distribution --- Characteristic functions --- Data processing --- 003.0727 --- informatique --- media --- statistiek --- Network analysis --- Network science --- Network theory --- Systems analysis --- System theory --- Mathematical optimization --- statistique --- Graphes, Théorie des. --- Graph theory --- Graphes aléatoires. --- Random graphs --- Computer networks --- Bioinformatics --- Réseaux d'ordinateurs --- Bioinformatique --- Computer communication systems. --- Probabilities. --- Statistics . --- Statistical physics. --- Dynamical systems. --- Probability --- Combinations --- Chance --- Least squares --- Risk --- Communication systems, Computer --- Computer communication systems --- Data networks, Computer --- ECNs (Electronic communication networks) --- Electronic communication networks --- Networks, Computer --- Teleprocessing networks --- Data transmission systems --- Digital communications --- Electronic systems --- Information networks --- Telecommunication --- Cyberinfrastructure --- Electronic data processing --- Network computers --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Distributed processing --- System analysis. --- System analysis - Statistical methods --- System theory. --- Graphes, Théorie des. --- Graphes aléatoires. --- Réseaux d'ordinateurs