Graphs and Networks
-15%
portes grátis
Graphs and Networks
Kingan, S. R.
John Wiley & Sons Inc
04/2022
288
Dura
Inglês
9781118937181
15 a 20 dias
524
Descrição não disponível.
List of Figures iv
Preface viii
Chapter 1. From Koenigsberg to Connectomes 1
1.1. Introduction 1
1.2. Isomorphism 18
1.3. Minors and Constructions 25
Chapter 2. Fundamental Topics 39
2.1. Trees 39
2.2. Distance 44
2.3. Degree Sequences 52
2.4. Matrices 56
Chapter 3. Similarity and Centrality 70
3.1. Similarity Measures 70
3.2. Centrality Measures 74
3.3. Eigenvector and Katz Centrality 78
3.4. PageRank 84
Chapter 4. Types of Networks 91
4.1. Small-World Networks 91
4.2. Scale-Free Networks 95
4.3. Assortative Mixing 97
4.4. Covert Networks 102
Chapter 5. Graph Algorithms 107
5.1. Traversal Algorithms 107
5.2. Greedy Algorithms 113
5.3. Shortest Path Algorithms 118
Chapter 6. Structure, Coloring, Higher Connectivity 126
6.1. Eulerian Circuits 126
6.2. Hamiltonian Cycles 131
6.3. Coloring 136
6.4. Higher Connectivity 142
6.5. Menger's Theorem 148
Chapter 7. Planar Graphs 159
7.1. Properties of Planar Graphs 159
7.2. Euclid's Theorem on Regular Polyhedra 167
7.3. The Five Color Theorem 172
7.4. Invariants for Non-Planar Graphs 174
Chapter 8. Flows and Matchings 182
8.1. Flows in Networks 182
8.2. Stable Sets, Matchings, Coverings 188
8.3. Min-Max Theorems 192
8.4. Maximum Matching Algorithm 196
Appendix A. Linear Algebra 211
Appendix B. Probability and Statistics 215
Appendix C. Complexity of Algorithms 218
Appendix D. Stacks and Queues 222
Appendix. Bibliography 226
Preface viii
Chapter 1. From Koenigsberg to Connectomes 1
1.1. Introduction 1
1.2. Isomorphism 18
1.3. Minors and Constructions 25
Chapter 2. Fundamental Topics 39
2.1. Trees 39
2.2. Distance 44
2.3. Degree Sequences 52
2.4. Matrices 56
Chapter 3. Similarity and Centrality 70
3.1. Similarity Measures 70
3.2. Centrality Measures 74
3.3. Eigenvector and Katz Centrality 78
3.4. PageRank 84
Chapter 4. Types of Networks 91
4.1. Small-World Networks 91
4.2. Scale-Free Networks 95
4.3. Assortative Mixing 97
4.4. Covert Networks 102
Chapter 5. Graph Algorithms 107
5.1. Traversal Algorithms 107
5.2. Greedy Algorithms 113
5.3. Shortest Path Algorithms 118
Chapter 6. Structure, Coloring, Higher Connectivity 126
6.1. Eulerian Circuits 126
6.2. Hamiltonian Cycles 131
6.3. Coloring 136
6.4. Higher Connectivity 142
6.5. Menger's Theorem 148
Chapter 7. Planar Graphs 159
7.1. Properties of Planar Graphs 159
7.2. Euclid's Theorem on Regular Polyhedra 167
7.3. The Five Color Theorem 172
7.4. Invariants for Non-Planar Graphs 174
Chapter 8. Flows and Matchings 182
8.1. Flows in Networks 182
8.2. Stable Sets, Matchings, Coverings 188
8.3. Min-Max Theorems 192
8.4. Maximum Matching Algorithm 196
Appendix A. Linear Algebra 211
Appendix B. Probability and Statistics 215
Appendix C. Complexity of Algorithms 218
Appendix D. Stacks and Queues 222
Appendix. Bibliography 226
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
isomorphism; graph substructures; graph operations; graph statistics; tress; degree sequences; Eulerian circuits; Hamiltonian cycles; planar graphs; colorings; matchings and coverings; network algorithms; random graphs; graph algorithms
List of Figures iv
Preface viii
Chapter 1. From Koenigsberg to Connectomes 1
1.1. Introduction 1
1.2. Isomorphism 18
1.3. Minors and Constructions 25
Chapter 2. Fundamental Topics 39
2.1. Trees 39
2.2. Distance 44
2.3. Degree Sequences 52
2.4. Matrices 56
Chapter 3. Similarity and Centrality 70
3.1. Similarity Measures 70
3.2. Centrality Measures 74
3.3. Eigenvector and Katz Centrality 78
3.4. PageRank 84
Chapter 4. Types of Networks 91
4.1. Small-World Networks 91
4.2. Scale-Free Networks 95
4.3. Assortative Mixing 97
4.4. Covert Networks 102
Chapter 5. Graph Algorithms 107
5.1. Traversal Algorithms 107
5.2. Greedy Algorithms 113
5.3. Shortest Path Algorithms 118
Chapter 6. Structure, Coloring, Higher Connectivity 126
6.1. Eulerian Circuits 126
6.2. Hamiltonian Cycles 131
6.3. Coloring 136
6.4. Higher Connectivity 142
6.5. Menger's Theorem 148
Chapter 7. Planar Graphs 159
7.1. Properties of Planar Graphs 159
7.2. Euclid's Theorem on Regular Polyhedra 167
7.3. The Five Color Theorem 172
7.4. Invariants for Non-Planar Graphs 174
Chapter 8. Flows and Matchings 182
8.1. Flows in Networks 182
8.2. Stable Sets, Matchings, Coverings 188
8.3. Min-Max Theorems 192
8.4. Maximum Matching Algorithm 196
Appendix A. Linear Algebra 211
Appendix B. Probability and Statistics 215
Appendix C. Complexity of Algorithms 218
Appendix D. Stacks and Queues 222
Appendix. Bibliography 226
Preface viii
Chapter 1. From Koenigsberg to Connectomes 1
1.1. Introduction 1
1.2. Isomorphism 18
1.3. Minors and Constructions 25
Chapter 2. Fundamental Topics 39
2.1. Trees 39
2.2. Distance 44
2.3. Degree Sequences 52
2.4. Matrices 56
Chapter 3. Similarity and Centrality 70
3.1. Similarity Measures 70
3.2. Centrality Measures 74
3.3. Eigenvector and Katz Centrality 78
3.4. PageRank 84
Chapter 4. Types of Networks 91
4.1. Small-World Networks 91
4.2. Scale-Free Networks 95
4.3. Assortative Mixing 97
4.4. Covert Networks 102
Chapter 5. Graph Algorithms 107
5.1. Traversal Algorithms 107
5.2. Greedy Algorithms 113
5.3. Shortest Path Algorithms 118
Chapter 6. Structure, Coloring, Higher Connectivity 126
6.1. Eulerian Circuits 126
6.2. Hamiltonian Cycles 131
6.3. Coloring 136
6.4. Higher Connectivity 142
6.5. Menger's Theorem 148
Chapter 7. Planar Graphs 159
7.1. Properties of Planar Graphs 159
7.2. Euclid's Theorem on Regular Polyhedra 167
7.3. The Five Color Theorem 172
7.4. Invariants for Non-Planar Graphs 174
Chapter 8. Flows and Matchings 182
8.1. Flows in Networks 182
8.2. Stable Sets, Matchings, Coverings 188
8.3. Min-Max Theorems 192
8.4. Maximum Matching Algorithm 196
Appendix A. Linear Algebra 211
Appendix B. Probability and Statistics 215
Appendix C. Complexity of Algorithms 218
Appendix D. Stacks and Queues 222
Appendix. Bibliography 226
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
