Читать книгу Graphs and Networks - S. R. Kingan - Страница 2

1  Cover

2  Title Page

3  Copyright

4  Dedication

5  List of Figures

6  Preface

7  1 From Königsberg to Connectomes 1.1 Introduction 1.2 Isomorphism 1.3 Constructions and Minors Exercises Topics for Deeper Study Notes

8  2 Fundamental Topics 2.1 Trees 2.2 Distance 2.3 Degree Sequences 2.4 Matrices Exercises Topics for Deeper Study Notes

9  3 Similarity and Centrality 3.1 Similarity Measures 3.2 Centrality Measures 3.3 Eigenvector and Katz Centrality 3.4 PageRank Exercises Topics for Deeper Study Notes

10  4 Types of Networks 4.1 Small‐World Networks 4.2 Scale‐Free Networks 4.3 Assortative Mixing 4.4 Covert Networks Exercises Topics for Deeper Study Notes

11  5 Graph Algorithms 5.1 Traversal Algorithms 5.2 Greedy Algorithms 5.3 Shortest Path Algorithms Exercises Topics for Deeper Study Notes

12  6 Structure, Coloring, Higher Connectivity 6.1 Eulerian Circuits 6.2 Hamiltonian Cycles 6.3 Coloring 6.4 Higher Connectivity 6.5 Menger's Theorem Exercises Topics for Deeper Study Notes

13  7 Planar Graphs 7.1 Properties of Planar Graphs 7.2 Euclid's Theorem on Regular Polyhedra 7.3 The Five Color Theorem 7.4 Invariants for Non‐planar Graphs Exercises Topics for Deeper Study Notes

14  8 Flows and Matchings 8.1 Flows in Networks 8.2 Stable Sets, Matchings, Coverings 8.3 Min–Max Theorems 8.4 Maximum Matching Algorithm Exercises Topics for Deeper Study Notes

15  Appendix A: Linear Algebra

16  Appendix B: Probability and Statistics

17  Appendix C: Complexity of Algorithms Notes

18  Appendix D: Stacks and Queues

19  Bibliography

20  Index

21  End User License Agreement