Statistical Analysis of Network Data

Methods and Models

By: Eric D. Kolaczyk

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Hardcover | 19 March 2009

At a Glance

Hardcover
404 Pages

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23.39 x 15.6 x 2.39

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In the past decade, the study of networks has increased dramatically. Researchers from across the sciences-including biology and bioinformatics, computer science, economics, engineering, mathematics, physics, sociology, and statistics-are more and more involved with the collection and statistical analysis of network-indexed data. As a result, statistical methods and models are being developed in this area at a furious pace, with contributions coming from a wide spectrum of disciplines.

This book provides an up-to-date treatment of the foundations common to the statistical analysis of network data across the disciplines. The material is organized according to a statistical taxonomy, although the presentation entails a conscious balance of concepts versus mathematics. In addition, the examples-including extended cases studies-are drawn widely from the literature. This book should be of substantial interest both to statisticians and to anyone else working in the area of 'network science.'

The coverage of topics in this book is broad, but unfolds in a systematic manner, moving from descriptive (or exploratory) methods, to sampling, to modeling and inference. Specific topics include network mapping, characterization of network structure, network sampling, and the modeling, inference, and prediction of networks, network processes, and network flows. This book is the first such resource to present material on all of these core topics in one place.

Industry Reviews

From the reviews:

"...Accessible and easy to read...strikes a balance between concepts and mathematical detail. ...This book is a superb introduction to a fascinating area." (International Statistical Review, 2010, 78, 1, 134-159) "Many disciplines are nowadays involved in network modeling, but it appears as if a common methodological foundation is lacking. The objective of this book is to provide a first attempt at defining such a common methodological foundation from a statistical point of view. ... The style of the writing is excellent. ... ample references allow quick access to further literature. I can recommend this book to anyone with a serious statistical interest in networks." (Fred van Eeuwijk, VOC Nieuwsbrief, Issue 44, May, 2010)

"Any reader interested in networks and wanting a perspective beyond that of any single discipline should acquire this book. ... Researchers will also appreciate the many points in the book where important open problems are identified. The book can also serve readily and flexibly as the main textbook for either a graduate-level seminar course or for an informally organized reading group. ... This book sets itself the challenge of addressing statistics for network science broadly, and in the many ways already noted, it is successful." (Michael Frey, Technometrics, Vol. 54 (1), February, 2012)

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Paperback

Published: 6th December 2010

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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
Table of Contents provided by Ingram. All Rights Reserved.

Statistical Analysis of Network Data

Methods and Models

At a Glance

Hardcover

Industry Reviews

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