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Graphentheorie und Netzwerkanalyse: Eine kompakte Einführung mit Beispielen, Übungen und Lösungsvorschlägen
by Christin SchmidtDieses Lehrbuch bietet eine kompakte Einführung in die Grundlagen der Graphentheorie und die Methoden der Netzwerkanalyse. Zahlreiche praktische Beispiele und Übungsaufgaben mit Lösungsvorschlägen helfen Leser:innen dabei, die theoretischen Konzepte besser zu verstehen und anzuwenden. Dabei werden unterschiedliche Technologien und Programmiersprachen verwendet, um ein breites Spektrum an Anwendungen abzudecken. Darüber hinaus beleuchten spezielle Kapitel die Methodik mit Blick auf die Planung und Durchführung eigener Netzwerkanalyseprojekte sowie ethische und datenschutzrechtliche Aspekte. So liefert das Buch nicht nur einen theoretischen Überblick, sondern auch praktische Tipps und Anleitungen für die Untersuchung eigener netzwerkanalytischer Fragestellungen. Dieses Buch eignet sich nicht nur als Nachschlagewerk für Studierende und Dozierende vielfältiger Fachdisziplinen mit curricularem Bezug zum Thema, sondern auch als Ergänzung des Repertoires von Praktiker:innen im Bereich Data Science mit Interesse an der Untersuchung von Netzwerken. Ob als theoretischer Einstieg oder als praktischer Ratgeber - dieses Buch leistet einen Beitrag für die Untersuchung und Analyse von Netzwerken und bietet eine Grundlage für weiterführende Studien und Projekte.
Graphentheorie: Eine elementare Einführung in Begriffe, Konzepte, Probleme und Algorithmen
by Jan Fricke Theo OverhagenDieses kompakte Lehrbuch führt in die grundlegenden Problemstellungen, Begriffe und Konzepte der Graphentheorie ein und liefert einen entsprechenden Überblick: In den ersten beiden Kapiteln werden die grundlegenden Begriffe geklärt – alle anderen Kapitel behandeln darauf aufbauend und weitgehend unabhängig voneinander jeweils einen wichtigen Problemkreis. Die Resultate und Lösungsalgorithmen werden dabei jeweils durch viele Beispiele, Grafiken und Übungsaufgaben veranschaulicht. Das Buch legt außerdem großen Wert auf die Erläuterung der Zusammenhänge; bis auf wenige Ausnahmen werden alle Resultate bewiesen. Zum Verständnis des Inhalts sind nur mathematische Grundkenntnisse nötig. Das Buch ist daher für Anfängervorlesungen in den ersten Semestern des Mathematikstudiums und insbesondere für Lehramtsstudierende gut geeignet. Es kann aber beispielsweise auch für Seminare, AGs oder Schülerprojekte verwendet werden.
Graphical Analysis of Multi-Response Data
by Kaye Enid Basford John Wilder TukeyA comprehensive summary of new and existing approaches to analyzing multiresponse data, Graphical Analysis of Multiresponse Data emphasizes graphical procedures. These procedures are then used, in various ways, to analyze, summarize, and present data from a specific, well-known plant breeding trial.These procedures result in overlap plots, their corresponding semigraphical tables, scatter plot matrices, profiles across environments and attributes for individual genotypes and groups of genotypes, and principal components.The interpretation of these displays, as an aid to understanding, is illustrated and discussed. Techniques for choosing expressions for the observed quantities are also emphasized.Graphical Analysis of Multiresponse Data is arranged into three parts:What can usefully be doneConsequences for the exampleApproaches and choices in more detailThat structure enables the reader to obtain an overview of what can be found, and to then delve into various aspects more deeply if desired. Statisticians, data analysts, biometricians, plant breeders, behavioral scientists, social scientists, and engineering scientists will find Graphical Analysis of Multiresponse Data offers invaluable assistance. Its details are also of interest to scientists in private firms, government institutions, and research organizations who are concerned with the analysis and interpretation of experimental multiresponse data.
Graphical Belief Modeling
by Russel .G AlmondThis innovative volume explores graphical models using belief functions as a representation of uncertainty, offering an alternative approach to problems where probability proves inadequate. Graphical Belief Modeling makes it easy to compare the two approaches while evaluating their relative strengths and limitations. The author examines both theory and computation, incorporating practical notes from the author's own experience with the BELIEF software package. As one of the first volumes to apply the Dempster-Shafer belief functions to a practical model, a substantial portion of the book is devoted to a single example--calculating the reliability of a complex system. This special feature enables readers to gain a thorough understanding of the application of this methodology.The first section provides a description of graphical belief models and probablistic graphical models that form an important subset: the second section discusses the algorithm used in the manipulation of graphical models: the final segment of the book offers a complete description of the risk assessment example, as well as the methodology used to describe it. Graphical Belief Modeling offers researchers and graduate students in artificial intelligence and statistics more than just a new approach to an old reliability task: it provides them with an invaluable illustration of the process of graphical belief modeling.
Graphical Data Analysis with R (Chapman & Hall/CRC The R Series #27)
by Antony UnwinSee How Graphics Reveal Information Graphical Data Analysis with R shows you what information you can gain from graphical displays. The book focuses on why you draw graphics to display data and which graphics to draw (and uses R to do so). All the datasets are available in R or one of its packages and the R code is available at rosuda.org/GDA. Graphical data analysis is useful for data cleaning, exploring data structure, detecting outliers and unusual groups, identifying trends and clusters, spotting local patterns, evaluating modelling output, and presenting results. This book guides you in choosing graphics and understanding what information you can glean from them. It can be used as a primary text in a graphical data analysis course or as a supplement in a statistics course. Colour graphics are used throughout.
Graphical Methods for Data Analysis
by J. M. ChambersThis book present graphical methods for analysing data. Some methods are new and some are old, some require a computer and others only paper and pencil; but they are all powerful data analysis tools. In many situations, a set of data � even a large set- can be adequately analysed through graphical methods alone. In most other situations, a few well-chosen graphical displays can significantly enhance numerical statistical analyses.
Graphical Models with R
by David Edwards Søren Højsgaard Steffen LauritzenGraphical models in their modern form have been around since the late 1970s and appear today in many areas of the sciences. Along with the ongoing developments of graphical models, a number of different graphical modeling software programs have been written over the years. In recent years many of these software developments have taken place within the R community, either in the form of new packages or by providing an R interface to existing software. This book attempts to give the reader a gentle introduction to graphical modeling using R and the main features of some of these packages. In addition, the book provides examples of how more advanced aspects of graphical modeling can be represented and handled within R. Topics covered in the seven chapters include graphical models for contingency tables, Gaussian and mixed graphical models, Bayesian networks and modeling high dimensional data.
Graphics for Statistics and Data Analysis with R (Chapman & Hall/CRC Texts in Statistical Science)
by Kevin J. Keen<p>Graphics for Statistics and Data Analysis with R, Second Edition, presents the basic principles of graphical design and applies these principles to engaging examples using the graphics and lattice packages in R. It offers a wide array of modern graphical displays for data visualization and representation. Added in the second edition are coverage of the ggplot2 graphics package, material on human visualization and color rendering in R, on screen, and in print. It emphasizes the fundamentals of statistical graphics and best practice guidelines for producing and choosing among graphical displays in R. <p>Provides downloadable R code and data for figures at www.graphicsforstatistics.com</p>
Graphics for Statistics and Data Analysis with R (Chapman & Hall/CRC Texts in Statistical Science)
by Kevin J. Keen<i>Graphics for Statistics and Data Analysis with R, Second Edition</i>, presents the basic principles of graphical design and applies these principles to engaging examples using the graphics and lattice packages in R. It offers a wide array of modern graphical displays for data visualization and representation. Added in the second edition are coverage of the ggplot2 graphics package, material on human visualization and color rendering in R, on screen, and in print.
Graphing Calculator Manual
by Mario F. Triola Kathleen Mclaughlin Dorothy WakefieldThis manual is organized to follow the sequence of topics in the textbook, and it is an easy-to-follow, step-by-step guide on how to use the TI-83/84 Plus graphing calculator. It provides worked-out examples to help students fully understand and use the graphing calculator.
Graphs & Digraphs (Textbooks in Mathematics)
by Ping Zhang Gary Chartrand Heather Jordon Vincent VatterGraphs & Digraphs, Seventh Edition masterfully employs student-friendly exposition, clear proofs, abundant examples, and numerous exercises to provide an essential understanding of the concepts, theorems, history, and applications of graph theory. This classic text, widely popular among students and instructors alike for decades, is thoroughly streamlined in this new, seventh edition, to present a text consistent with contemporary expectations. Changes and updates to this edition include: • A rewrite of four chapters from the ground up. • Streamlining by over a third for efficient, comprehensive coverage of graph theory. • Flexible structure with foundational Chapters 1–6 and customizable topics in Chapters 7–11. • Incorporation of the latest developments in fundamental graph theory. • Statements of recent groundbreaking discoveries, even if proofs are beyond scope. • Completely reorganized chapters on traversability, connectivity, coloring, and extremal graph theory to reflect recent developments. The text remains the consummate choice for an advanced undergraduate level or introductory graduate-level course exploring the subject’s fascinating history, while covering a host of interesting problems and diverse applications. Our major objective is to introduce and treat graph theory as the beautiful area of mathematics we have always found it to be. We have striven to produce a reader-friendly, carefully written book that emphasizes the mathematical theory of graphs, in all their forms. While a certain amount of mathematical maturity, including a solid understanding of proof, is required to appreciate the material, with a small number of exceptions this is the only pre-requisite. In addition, owing to the exhilarating pace of progress in the field, there have been countless developments in fundamental graph theory ever since the previous edition, and many of these discoveries have been incorporated into the book. Of course, some of the proofs of these results are beyond the scope of the book, in which cases we have only included their statements. In other cases, however, these new results have led us to completely reorganize our presentation. Two examples are the chapters on coloring and extremal graph theory.
Graphs Theory and Applications: With Exercises and Problems (Wiley-iste Ser.)
by Jean-Claude FournierThis book provides a pedagogical and comprehensive introduction to graph theory and its applications. It contains all the standard basic material and develops significant topics and applications, such as: colorings and the timetabling problem, matchings and the optimal assignment problem, and Hamiltonian cycles and the traveling salesman problem, to name but a few. Exercises at various levels are given at the end of each chapter, and a final chapter presents a few general problems with hints for solutions, thus providing the reader with the opportunity to test and refine their knowledge on the subject. An appendix outlines the basis of computational complexity theory, in particular the definition of NP-completeness, which is essential for algorithmic applications.
Graphs and Combinatorial Optimization: CTW 2023, Garmisch-Partenkirchen, Germany, June 20–22 (AIRO Springer Series #13)
by Stefan Pickl Andreas Brieden Markus SiegleThis book contains the proceedings of the 19th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, held during June 20-22, 2023, in Garmisch-Partenkirchen, Germany. This successful series of international workshops is known to attract high-quality research on the theory and application of discrete algorithms, graphs, and combinatorial optimization in a wide sense. The papers collected in this book represent cutting-edge research by leading researchers and attract a broad readership in academia worldwide. The book is addressed to researchers and advanced students, but also to professionals in industry concerned with algorithm design and optimization problems in different areas of application.
Graphs and Combinatorial Optimization: CTW2020 Proceedings (AIRO Springer Series #5)
by Claudio Gentile Giuseppe Stecca Paolo VenturaThis book highlights new and original contributions on Graph Theory and Combinatorial Optimization both from the theoretical point of view and from applications in all fields. The book chapters describe models and methods based on graphs, structural properties, discrete optimization, network optimization, mixed-integer programming, heuristics, meta-heuristics, math-heuristics, and exact methods as well as applications. The book collects selected contributions from the CTW2020 international conference (18th Cologne-Twente Workshop on Graphs and Combinatorial Optimization), held online on September 14-16, 2020. The conference was organized by IASI-CNR with the contribution of University of Roma Tre, University Roma Tor Vergata, and CNRS-LIX and with the support of AIRO. It is addressed to researchers, PhD students, and practitioners in the fields of Graph Theory, Discrete Mathematics, Combinatorial Optimization, and Operations Research.
Graphs and Matrices
by Ravindra B. BapatThis 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.
Graphs for the Analysis of Bipolar Fuzzy Information (Studies in Fuzziness and Soft Computing #401)
by Muhammad Akram Musavarah Sarwar Wieslaw A. DudekThis monograph discusses decision making methods under bipolar fuzzy graphical models with the aim of overcoming the lack of mathematical approach towards bipolar information—positive and negative. It investigates the properties of bipolar fuzzy graphs, their distance functions, and concept of their isomorphism. It presents certain notions, including irregular bipolar fuzzy graphs, domination in bipolar fuzzy graphs, bipolar fuzzy circuits, energy in bipolar fuzzy graphs, bipolar single-valued neutrosophic competition graphs, and bipolar neutrosophic graph structures. This book also presents the applications of mentioned concepts to real-world problems in areas of product manufacturing, international relations, psychology, global terrorism and more, making it valuable for researchers, computer scientists, social scientists and alike.
Graphs in Biomedical Image Analysis, and Overlapped Cell on Tissue Dataset for Histopathology: 5th MICCAI Workshop, GRAIL 2023 and 1st MICCAI Challenge, OCELOT 2023, Held in Conjunction with MICCAI 2023, Vancouver, BC, Canada, September 23, and October 4, 2023, Proceedings (Lecture Notes in Computer Science #14373)
by Seyed-Ahmad Ahmadi Sérgio PereiraThis LNCS conference volume constitutes the proceedings of the MICCAI Workshop GRAIL 2023 and MICCAI Challenge OCELOT 2023, Held in Conjunction with MICCAI 2023, Vancouver, BC, Canada, September 23, and October 4, 2023. The 9 full papers (GRAIL 2023) and 6 full papers (OCELOT 2023) included in this volume were carefully reviewed and selected from GRAIL 14 (GRAIL 2023) and 6 (OCELOT 2023) submissions. The conference GRAIL 2023 a wide set of methods and application and OCELOT 2023 focuses on the cover a wide range of methods utilizing tissue information for better cell detection, in the sense of training strategy, model architecture, and especially how to model cell-tissue relationships.
Graphs in Biomedical Image Analysis: 6th International Workshop, GRAIL 2024, Held in Conjunction with MICCAI 2024, Marrakesh, Morocco, October 6, 2024, Proceedings (Lecture Notes in Computer Science #15182)
by Seyed-Ahmad Ahmadi Anees KaziThis book constitutes the refereed proceedings of the 6th International Workshop on Graphs in Biomedical Image Analysis, GRAIL 2024, held in conjunction with MICCAI 2024, in Marrakesh, Morocco, on October 6, 2024. The 12 full papers included in this volume were carefully reviewed and selected from 19 submissions. The papers cover a wide range of topics, such as deep/machine learning on graphs; probabilistic graphical models for biomedical data analysis; signal processing on graphs for biomedical image analysis; explainable AI (XAI) methods in geometric deep learning; big data analysis with graphs; graphs for small data sets; semantic graph research in medicine; modeling and applications of graph symmetry/equivariance; or graph generative models.
Graphs in Perturbation Theory: Algebraic Structure And Asymptotics (Springer Theses)
by Michael BorinskyThis book is the first systematic study of graphical enumeration and the asymptotic algebraic structures in perturbative quantum field theory. Starting with an exposition of the Hopf algebra structure of generic graphs, it reviews and summarizes the existing literature. It then applies this Hopf algebraic structure to the combinatorics of graphical enumeration for the first time, and introduces a novel method of asymptotic analysis to answer asymptotic questions. This major breakthrough has combinatorial applications far beyond the analysis of graphical enumeration. The book also provides detailed examples for the asymptotics of renormalizable quantum field theories, which underlie the Standard Model of particle physics. A deeper analysis of such renormalizable field theories reveals their algebraic lattice structure. The pedagogical presentation allows readers to apply these new methods to other problems, making this thesis a future classic for the study of asymptotic problems in quantum fields, network theory and far beyond.
Graphs on Surfaces: Dualities, Polynomials, and Knots
by Joanna A. Ellis-Monaghan Iain MoffattGraphs on Surfaces: Dualities, Polynomials, and Knots offers an accessible and comprehensive treatment of recent developments on generalized duals of graphs on surfaces, and their applications. The authors illustrate the interdependency between duality, medial graphs and knots; how this interdependency is reflected in algebraic invariants of graphs and knots; and how it can be exploited to solve problems in graph and knot theory. Taking a constructive approach, the authors emphasize how generalized duals and related ideas arise by localizing classical constructions, such as geometric duals and Tait graphs, and then removing artificial restrictions in these constructions to obtain full extensions of them to embedded graphs. The authors demonstrate the benefits of these generalizations to embedded graphs in chapters describing their applications to graph polynomials and knots. Graphs on Surfaces: Dualities, Polynomials, and Knots also provides a self-contained introduction to graphs on surfaces, generalized duals, topological graph polynomials, and knot polynomials that is accessible both to graph theorists and to knot theorists. Directed at those with some familiarity with basic graph theory and knot theory, this book is appropriate for graduate students and researchers in either area. Because the area is advancing so rapidly, the authors give a comprehensive overview of the topic and include a robust bibliography, aiming to provide the reader with the necessary foundations to stay abreast of the field. The reader will come away from the text convinced of advantages of considering these higher genus analogues of constructions of plane and abstract graphs, and with a good understanding of how they arise.
Graphs!
by David A. AdlerMath booster author David A. Adler and artist Ed Miller make pie charts easy-as-pie charts with this fun and vibrantly illustrated guide to data collection.For students, STEM topics don&’t always feel like a walk in the park. But what if they were more like a day at the fair? Follow Janet and Ben from the Ferris Wheel to the carousel as they use graphs and data collection to make decisions about their day. This is the sixteenth book in this duo&’s math picture book series. Combining elements of a graphic story with engaging and accessible nonfiction text, David A. Adler combines his well-established STEM know-how with Edward Miller&’s vibrant, high contrast art to take young readers on a wild ride through the world of bar graphs, pictographs, pie charts, and more!
Graphs, Algorithms, and Optimization (Discrete Mathematics and Its Applications)
by William Kocay Donald L. Kreher<p>Graph theory offers a rich source of problems and techniques for programming and data structure development, as well as for understanding computing theory, including NP-Completeness and polynomial reduction. A comprehensive text, Graphs, Algorithms, and Optimization features clear exposition on modern algorithmic graph theory presented in a rigorous yet approachable way. The book covers major areas of graph theory including discrete optimization and its connection to graph algorithms. The authors explore surface topology from an intuitive point of view and include detailed discussions on linear programming that emphasize graph theory problems useful in mathematics and computer science. Many algorithms are provided along with the data structure needed to program the algorithms efficiently. <p>The book also provides coverage on algorithm complexity and efficiency, NP-completeness, linear optimization, and linear programming and its relationship to graph algorithms.Written in an accessible and informal style, this work covers nearly all areas of graph theory. Graphs, Algorithms, and Optimization provides a modern discussion of graph theory applicable to mathematics, computer science, and crossover applications.</p>
Graphs, Algorithms, and Optimization (Discrete Mathematics and Its Applications)
by William Kocay Donald L. KreherThe second edition of this popular book presents the theory of graphs from an algorithmic viewpoint. The authors present the graph theory in a rigorous, but informal style and cover most of the main areas of graph theory. The ideas of surface topology are presented from an intuitive point of view. We have also included a discussion on linear programming that emphasizes problems in graph theory. The text is suitable for students in computer science or mathematics programs.
Graphs, Matrices, and Designs: Festschrift In Honor Of Norman J. Pullman
by ReesExamines partitions and covers of graphs and digraphs, latin squares, pairwise balanced designs with prescribed block sizes, ranks and permanents, extremal graph theory, Hadamard matrices and graph factorizations. This book is designed to be of interest to applied mathematicians, computer scientists and communications researchers.
Graphs, Networks and Algorithms
by Dieter JungnickelFrom the reviews of the previous editions ".... The book is a first class textbook and seems to be indispensable for everybody who has to teach combinatorial optimization. It is very helpful for students, teachers, and researchers in this area. The author finds a striking synthesis of nice and interesting mathematical results and practical applications. ... the author pays much attention to the inclusion of well-chosen exercises. The reader does not remain helpless; solutions or at least hints are given in the appendix. Except for some small basic mathematical and algorithmic knowledge the book is self-contained. ..." K.Engel, Mathematical Reviews 2002 The substantial development effort of this text, involving multiple editions and trailing in the context of various workshops, university courses and seminar series, clearly shows through in this new edition with its clear writing, good organisation, comprehensive coverage of essential theory, and well-chosen applications. The proofs of important results and the representation of key algorithms in a Pascal-like notation allow this book to be used in a high-level undergraduate or low-level graduate course on graph theory, combinatorial optimization or computer science algorithms. The well-worked solutions to exercises are a real bonus for self study by students. The book is highly recommended. P .B. Gibbons, Zentralblatt für Mathematik 2005 Once again, the new edition has been thoroughly revised. In particular, some further material has been added: more on NP-completeness (especially on dominating sets), a section on the Gallai-Edmonds structure theory for matchings, and about a dozen additional exercises - as always, with solutions. Moreover, the section on the 1-factor theorem has been completely rewritten: it now presents a short direct proof for the more general Berge-Tutte formula. Several recent research developments are discussed and quite a few references have been added.