Statistical Analysis of Network Data: Methods and Models

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Springer Science & Business Media, 20 avr. 2009 - 386 pages
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In recent years there has been an explosion of network data – that is, measu- ments that are either of or from a system conceptualized as a network – from se- ingly all corners of science. The combination of an increasingly pervasive interest in scienti c analysis at a systems level and the ever-growing capabilities for hi- throughput data collection in various elds has fueled this trend. Researchers from biology and bioinformatics to physics, from computer science to the information sciences, and from economics to sociology are more and more engaged in the c- lection and statistical analysis of data from a network-centric perspective. Accordingly, the contributions to statistical methods and modeling in this area have come from a similarly broad spectrum of areas, often independently of each other. Many books already have been written addressing network data and network problems in speci c individual disciplines. However, there is at present no single book that provides a modern treatment of a core body of knowledge for statistical analysis of network data that cuts across the various disciplines and is organized rather according to a statistical taxonomy of tasks and techniques. This book seeks to ll that gap and, as such, it aims to contribute to a growing trend in recent years to facilitate the exchange of knowledge across the pre-existing boundaries between those disciplines that play a role in what is coming to be called ‘network science.
 

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Table des matières

643 Fitting Network Growth Models
178
65 Exponential Random Graph Models
180
652 Fitting Exponential Random Graph Models
185
653 GoodnessofFit and Model Degeneracy
187
Modeling Collaboration Among Lawyers
188
66 Challenges in Modeling Network Graphs
191
67 Additional Related Topics and Reading
193
Exercises
195

212 Families of Graphs
18
213 Graphs and Matrix Algebra
20
214 Graph Data Structures and Algorithms
21
22 Background in Probability and Statistics
24
221 Probability
25
222 Principles of Statistical Inference
31
Tutorials
32
Prelude
42
24 Additional Related Topics and Reading
45
Mapping Networks
49
32 Collecting Relational Network Data
50
321 Measurement of System Elements and Interactions
51
322 Enumerated Partial and Sampled Data
54
33 Constructing Network Graph Representations
56
34 Visualizing Network Graphs
58
342 Methods of Graph Visualization
60
35 Case Studies
63
351 Mapping Science
65
352 Mapping the Internet
68
36 Mapping Dynamic Networks
74
37 Additional Related Topics and Reading
76
Exercises
77
Descriptive Analysis of Network Graph Characteristics
79
42 Vertex and Edge Characteristics
80
422 Centrality
88
43 Characterizing Network Cohesion
94
432 Connectivity
97
433 Graph Partitioning
102
434 Assortativity and Mixing
111
Analysis of an Epileptic Seizure
114
45 Characterizing Dynamic Network Graphs
116
46 Additional Related Topics and Reading
119
Exercises
120
Sampling and Estimation in Network Graphs
123
52 Background on Statistical Sampling Theory
126
522 Estimation of Group Size
129
53 Common Network Graph Sampling Designs
131
532 Star and Snowball Sampling
133
533 Link Tracing
136
54 Estimation of Totals in Network Graphs
137
542 Totals on Vertex Pairs
138
543 Totals of Higher Order
141
544 Effects of Design Measurement and Total
143
55 Estimation of Network Group Size
145
56 Other Network Graph Estimation Problems
149
57 Additional Related Topics and Reading
151
Models for Network Graphs
153
62 Random Graph Models
154
621 Classical Random Graph Models
156
622 Generalized Random Graph Models
158
623 Simulating Random Graph Models
159
624 Statistical Application of Random Graph Models
162
63 SmallWorld Models
169
632 Other SmallWorld Network Models
171
64 Network Growth Models
172
641 Preferential Attachment Models
173
642 Copying Models
176
Network Topology Inference
197
72 Link Prediction
199
721 Informal Scoring Methods
201
722 Probabilistic Classification Methods
202
Predicting Lawyer Collaboration
205
73 Inference of Association Networks
207
731 Correlation Networks
209
732 Partial Correlation Networks
212
733 Gaussian Graphical Model Networks
216
Inferring Genetic Regulatory Interactions
220
74 Tomographic Network Topology Inference
223
741 Tomographic Inference of Tree Topologies
225
742 Methods Based on Hierarchical Clustering
228
743 Likelihoodbased Methods
231
744 Summarizing Collections of Trees
234
Computer Network Topology Identification
236
75 Additional Related Topics and Reading
241
Exercises
242
Modeling and Prediction for Processes on Network Graphs
245
82 Nearest Neighbor Prediction
246
83 Markov Random Fields
249
832 Inference and Prediction for Markov Random Fields
252
833 Related Probabilistic Models
256
84 Kernelbased Regression
257
841 Kernel Regression on Graphs
258
842 Designing Kernels on Graphs
262
Predicting Protein Function
266
86 Modeling and Prediction for Dynamic Processes
271
An Illustration
272
862 Other Dynamic Processes
280
87 Additional Related Topics and Reading
281
Exercises
282
Analysis of Network Flow Data
285
92 Gravity Models
287
921 Model Specification
288
922 Inference for Gravity Models
292
93 Traffic Matrix Estimation
297
931 Static Methods
298
932 Dynamic Methods
306
Internet Traffic Matrix Estimation
310
94 Estimation of Network Flow Costs
316
941 Link Costs from Endtoend Measurements
317
942 Path Costs from Endtoend Measurements
321
95 Additional Related Topics and Reading
328
Exercises
330
Graphical Models
333
102 Defining Graphical Models
334
1021 Directed Graphical Models
335
1022 Undirected Graphical Models
339
103 Inference for Graphical Models
342
104 Additional Related Topics and Reading
344
Glossary of Notation
345
References
347
Author Index
373
Subject Index
381
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