Graphs and Networks. S. R. Kingan

      

      Table of Contents

      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

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