| Introduction and Overview | p. 1 |
| Why Networks? | p. 1 |
| Examples of Networks | p. 3 |
| Technological Networks | p. 3 |
| Social Networks | p. 5 |
| Biological Networks | p. 7 |
| Information Networks | p. 9 |
| About this Book | p. 11 |
| Preliminaries | p. 15 |
| Background on Graphs | p. 15 |
| Basic Definitions and Concepts | p. 16 |
| Families of Graphs | p. 18 |
| Graphs and Matrix Algebra | p. 20 |
| Graph Data Structures and Algorithms | p. 21 |
| Background in Probability and Statistics | p. 24 |
| Probability | p. 25 |
| Principles of Statistical Inference | p. 31 |
| Methods of Statistical Inference: Tutorials | p. 32 |
| Statistical Analysis of Network Data: Prelude | p. 42 |
| Additional Related Topics and Reading | p. 45 |
| Exercises | p. 45 |
| Mapping Networks | p. 49 |
| Introduction | p. 49 |
| Collecting Relational Network Data | p. 50 |
| Measurement of System Elements and Interactions | p. 51 |
| Enumerated, Partial, and Sampled Data | p. 54 |
| Constructing Network Graph Representations | p. 56 |
| Visualizing Network Graphs | p. 58 |
| Elements of Graph Visualization | p. 58 |
| Methods of Graph Visualization | p. 60 |
| Case Studies | p. 63 |
| Mapping 'Science' | p. 65 |
| Mapping the Internet | p. 68 |
| Mapping Dynamic Networks | p. 74 |
| Additional Related Topics and Reading | p. 76 |
| Exercises | p. 77 |
| Descriptive Analysis of Network Graph Characteristics | p. 79 |
| Introduction | p. 79 |
| Vertex and Edge Characteristics | p. 80 |
| Degree | p. 80 |
| Centrality | p. 80 |
| Characterizing Network Cohesion | p. 94 |
| Local Density | p. 94 |
| Connectivity | p. 97 |
| Graph Partitioning | p. 102 |
| Assortativity and Mixing | p. 111 |
| Case Study: Analysis of an Epileptic Seizure | p. 114 |
| Characterizing Dynamic Network Graphs | p. 116 |
| Additional Related Topics and Reading | p. 119 |
| Exercise | p. 120 |
| Sampling and Estimation in Network Graphs | p. 123 |
| Introduction | p. 123 |
| Background on Statistical Sampling Theory | p. 126 |
| Horvitz-Thompson Estimation for Totals | p. 126 |
| Estimation of Group Size | p. 129 |
| Common Network Graph Sampling Designs | p. 131 |
| Induced and Incident Subgraph Sampling | p. 131 |
| Star and Snowball Sampling | p. 133 |
| Link Tracing | p. 136 |
| Estimation of Totals in Network Graphs | p. 137 |
| Vertex Totals | p. 137 |
| Totals on Vertex Pairs | p. 138 |
| Totals of Higher Order | p. 141 |
| Effects of Design, Measurement, and Total | p. 143 |
| Estimation of Network Group Size | p. 145 |
| Other Network Graph Estimation Problems | p. 149 |
| Additional Related Topics and Reading | p. 151 |
| Exercises | p. 151 |
| Models for Network Graphs | p. 153 |
| Introduction | p. 153 |
| Random Graph Models | p. 154 |
| Classical Random Graph Models | p. 156 |
| Generalized Random Graph Models | p. 158 |
| Simulating Random Graph Models | p. 159 |
| Statistical Application of Random Graph Models | p. 162 |
| Small-World Models | p. 169 |
| The Watts-Strogatz Model | p. 169 |
| Other Small-World Network Models | p. 171 |
| Network Growth Models | p. 172 |
| Preferential Attachment Models | p. 173 |
| Copying Models | p. 176 |
| Fitting Network Growth Models | p. 178 |
| Exponential Random Graph Models | p. 180 |
| Model Specification | p. 180 |
| Fitting Exponential Random Graph Models | p. 185 |
| Goodness-of-Fit and Model Degeneracy | p. 187 |
| Case Study: Modeling Collaboration Among Lawyers | p. 188 |
| Challenges in Modeling Network Graphs | p. 191 |
| Additional Related Topics and Reading | p. 193 |
| Exercises | p. 195 |
| Network Topology Inference | p. 197 |
| Introduction | p. 197 |
| Link Prediction | p. 199 |
| Informal Scoring Methods | p. 201 |
| Probabilistic Classification Methods | p. 202 |
| Case Study: Predicting Lawyer Collaboration | p. 205 |
| Inference of Association Networks | p. 207 |
| Correlation Networks | p. 209 |
| Partial Correlation Networks | p. 212 |
| Gaussian Graphical Model Networks | p. 216 |
| Case Study: Inferring Genetic Regulatory Interactions | p. 220 |
| Tomographic Network Topology Inference | p. 223 |
| Tomographic Inference of Tree Topologies | p. 225 |
| Methods Based on Hierarchical Clustering | p. 228 |
| Likelihood-based Methods | p. 231 |
| Summarizing Collections of Trees | p. 234 |
| Case Study: Computer Network Topology Identification | p. 236 |
| Additional Related Topics and Reading | p. 241 |
| Exercises | p. 242 |
| Modeling and Prediction for Processes on Network Graphs | p. 245 |
| Introduction | p. 245 |
| Nearest Neighbor Prediction | p. 246 |
| Markov Random Fields | p. 249 |
| Markov Random Field Models | p. 249 |
| Inference and Prediction for Markov Random Fields | p. 252 |
| Related Probabilistic Models | p. 256 |
| Kernel-based Regression | p. 257 |
| Kernel Regression on Graphs | p. 258 |
| Designing Kernels on Graphs | p. 262 |
| Case Study: Predicting Protein Function | p. 266 |
| Modeling and Prediction for Dynamic Processes | p. 271 |
| Epidemic Processes: An Illustration | p. 272 |
| Other Dynamic Processes | p. 280 |
| Additional Related Topics and Reading | p. 281 |
| Exercises | p. 282 |
| Analysis of Network Flow Data | p. 285 |
| Introduction | p. 285 |
| Gravity Models | p. 287 |
| Model Specification | p. 288 |
| Inference for Gravity Models | p. 292 |
| Traffic Matrix Estimation | p. 297 |
| Static Methods | p. 298 |
| Dynamic Methods | p. 306 |
| Case Study: Internet Traffic Matrix Estimation | p. 310 |
| Estimation of Network Flow Costs | p. 316 |
| Link Costs from End-to-end Measurements | p. 317 |
| Path Costs from End-to-end Measurements | p. 321 |
| Additional Related Topics and Reading | p. 328 |
| Exercises | p. 330 |
| Graphical Models | p. 333 |
| Introduction | p. 333 |
| Defining Graphical Models | p. 334 |
| Directed Graphical Models | p. 335 |
| Undirected Graphical Models | p. 339 |
| Inference for Graphical Models | p. 342 |
| Additional Related Topics and Reading | p. 344 |
| Glossary of Notation | p. 345 |
| References | p. 347 |
| Author Index | p. 373 |
| Subject Index | p. 381 |
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