Hypergraph theory : an introduction
This book presents hypergraph theory and covers traditional elements of the theory as well as original concepts such as entropy of hypergraph, similarities and kernels. It details applications in telecommunications and parallel data structure modeling.
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| Hlavní autor: | |
|---|---|
| Médium: | E-kniha Kniha |
| Jazyk: | angličtina |
| Vydáno: |
Cham
Springer
2013
Springer International Publishing AG Springer International Publishing |
| Vydání: | 1 |
| Edice: | Mathematical Engineering |
| Témata: | |
| ISBN: | 9783319000794, 3319000799, 3319033700, 9783319033709 |
| ISSN: | 2192-4732, 2192-4740 |
| On-line přístup: | Získat plný text |
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| Abstract | This book presents hypergraph theory and covers traditional elements of the theory as well as original concepts such as entropy of hypergraph, similarities and kernels. It details applications in telecommunications and parallel data structure modeling. |
|---|---|
| AbstractList | This book provides an introduction to hypergraphs, its aim being to overcome the lack of recent manuscripts on this theory. In the literature hypergraphs have many other names such as set systems and families of sets. This work presents the theory of hypergraphs in its most original aspects, while also introducing and assessing the latest concepts on hypergraphs.
The variety of topics, their originality and novelty are intended to help readers better understand the hypergraphs in all their diversity in order to perceive their value and power as mathematical tools.
This book will be a great asset to upper-level undergraduate and graduate students in computer science and mathematics. It has been the subject of an annual Master's course for many years, making it also ideally suited to Master's students in computer science, mathematics, bioinformatics, engineering, chemistry, and many other fields. It will also benefit scientists, engineers and anyone else who wants to understand hypergraphs theory. This book provides an introduction to hypergraphs, its aim being to overcome the lack of recent manuscripts on this theory. In the literature hypergraphs have many other names such as set systems and families of sets. This work presents the theory of hypergraphs in its most original aspects, while also introducing and assessing the latest concepts on hypergraphs. The variety of topics, their originality and novelty are intended to help readers better understand the hypergraphs in all their diversity in order to perceive their value and power as mathematical tools. This book will be a great asset to upper-level undergraduate and graduate students in computer science and mathematics. It has been the subject of an annual Master's course for many years, making it also ideally suited to Master's students in computer science, mathematics, bioinformatics, engineering, chemistry, and many other fields. It will also benefit scientists, engineers and anyone else who wants to understand hypergraphs theory. This book presents hypergraph theory and covers traditional elements of the theory as well as original concepts such as entropy of hypergraph, similarities and kernels. It details applications in telecommunications and parallel data structure modeling. |
| Author | Bretto, Alain |
| Author_xml | – sequence: 1 fullname: Bretto, Alain |
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| Copyright | Springer International Publishing Switzerland 2013 Distributed under a Creative Commons Attribution 4.0 International License |
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| Notes | Includes bibliographical references and index |
| OCLC | 849285856 |
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| PageCount | 129 |
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| PublicationYear | 2013 |
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| Snippet | This book presents hypergraph theory and covers traditional elements of the theory as well as original concepts such as entropy of hypergraph, similarities and... This book provides an introduction to hypergraphs, its aim being to overcome the lack of recent manuscripts on this theory. In the literature hypergraphs have... |
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| SubjectTerms | Algorithms Artificial Intelligence Communications Engineering, Networks Computer Science Data Structures and Algorithms Discrete Mathematics in Computer Science Document and Text Processing Engineering Graph Theory Hypergraphs Mathematical and Computational Engineering Mathematics |
| TableOfContents | 6.3 Hypercycles in a Dirhypergraph -- 6.4 Algebraic Representation of Dirhypergraphs -- 6.4.1 Dirhypergraphs Isomorphism -- 6.4.2 Algebraic Representation: Definition -- 6.4.3 Algebraic Representation Isomorphism -- References -- 7 Applications of Hypergraph Theory: A Brief Overview -- 7.1 Hypergraph Theory and System Modeling for Engineering -- 7.1.1 Chemical Hypergraph Theory -- 7.1.2 Hypergraph Theory for Telecomunmications -- 7.1.3 Hypergraph Theory and Parallel Data Structures -- 7.1.4 Hypergraphs and Constraint Satisfaction Problems -- 7.1.5 Hypergraphs and Database Schemes -- 7.1.6 Hypergraphs and Image Processing -- 7.1.7 Other Applications -- References -- Index Intro -- Preface -- Acknowledgments -- Contents -- 1 Hypergraphs: Basic Concepts -- 1.1 First Definitions -- 1.2 Example of Hypergraph -- 1.2.1 Simple Reduction Hypergraph Algorithm -- 1.3 Algebraic Definitions for Hypergraphs -- 1.3.1 Matrices, Hypergraphs and Entropy -- 1.3.2 Similarity and Metric on Hypergraphs -- 1.3.3 Hypergraph Morphism -- Groups and Symmetries -- 1.4 Generalization of Hypergraphs -- References -- 2 Hypergraphs: First Properties -- 2.1 Graphs versus Hypergraphs -- 2.1.1 Graphs -- 2.1.2 Graphs and Hypergraphs -- 2.2 Intersecting Families, Helly Property -- 2.2.1 Intersecting Families -- 2.2.2 Helly Property -- 2.3 Subtree Hypergraphs -- 2.4 Conformal Hypergraphs -- 2.5 Stable (or Independent), Transversal and Matching -- 2.5.1 Examples: -- 2.6 König Property and Dual König Property -- 2.7 linear Spaces -- References -- 3 Hypergraph Colorings -- 3.1 Coloring -- 3.2 Particular Colorings -- 3.2.1 Strong Coloring -- 3.2.2 Equitable Coloring -- 3.2.3 Good Coloring -- 3.2.4 Uniform Coloring -- 3.2.5 Hyperedge Coloring -- 3.2.6 Bicolorable Hypergraphs -- 3.3 Graph and Hypergraph Coloring Algorithm -- References -- 4 Some Particular Hypergraphs -- 4.1 Interval Hypergraphs -- 4.2 Unimodular Hypergraphs -- 4.2.1 Unimodular Hypergraphs and Discrepancy of Hypergraphs -- 4.3 Balanced Hypergraphs -- 4.4 Normal Hypergraphs -- 4.5 Arboreal Hypergraphs, Acyclicity and Hypertree Decomposition -- 4.5.1 Acyclic Hypergraph -- 4.5.2 Arboreal and Co-Arboreal Hypergraphs -- 4.5.3 Tree and Hypertree Decomposition -- 4.6 Planar Hypergraphs -- References -- 5 Reduction-Contraction of Hypergraph -- 5.1 Introduction -- 5.2 Reduction Algorithms -- 5.2.1 A Generic Algorithm -- 5.2.2 A Minimum Spanning Tree Algorithm (HR-MST) -- References -- 6 Dirhypergraphs: Basic Concepts -- 6.1 Basic Definitions -- 6.2 Basic Properties of Directed Hypergraphs |
| Title | Hypergraph theory : an introduction |
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