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Advances in Network Clustering and Blockmodeling. Edition No. 1. Wiley Series in Computational and Quantitative Social Science

  • ID: 5224758
  • Book
  • February 2020
  • 432 Pages
  • John Wiley and Sons Ltd

Provides an overview of the developments and advances in the field of network clustering and blockmodeling over the last 10 years

This book offers an integrated treatment of network clustering and blockmodeling, covering all of the newest approaches and methods that have been developed over the last decade. Presented in a comprehensive manner, it offers the foundations for understanding network structures and processes, and features a wide variety of new techniques addressing issues that occur during the partitioning of networks across multiple disciplines such as community detection, blockmodeling of valued networks, role assignment, and stochastic blockmodeling.

Written by a team of international experts in the field, Advances in Network Clustering and Blockmodeling offers a plethora of diverse perspectives covering topics such as: bibliometric analyses of the network clustering literature; clustering approaches to networks; label propagation for clustering; and treating missing network data before partitioning. It also examines the partitioning of signed networks, multimode networks, and linked networks. A chapter on structured networks and coarsegrained descriptions is presented, along with another on scientific coauthorship networks. The book finishes with a section covering conclusions and directions for future work. In addition, the editors provide numerous tables, figures, case studies, examples, datasets, and more.

  • Offers a clear and insightful look at the state of the art in network clustering and blockmodeling
  • Provides an excellent mix of mathematical rigor and practical application in a comprehensive manner
  • Presents a suite of new methods, procedures, algorithms for partitioning networks, as well as new techniques for visualizing matrix arrays
  • Features numerous examples throughout, enabling readers to gain a better understanding of research methods and to conduct their own research effectively
  • Written by leading contributors in the field of spatial networks analysis

Advances in Network Clustering and Blockmodeling is an ideal book for graduate and undergraduate students taking courses on network analysis or working with networks using real data. It will also benefit researchers and practitioners interested in network analysis.

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List of Contributors xv

1 Introduction 1
Patrick Doreian, Vladimir Batagelj, and Anuška Ferligoj

1.1 On the Chapters 1

1.2 Looking Forward 9

2 Bibliometric Analyses of the Network Clustering Literature 11
Vladimir Batagelj, Anuška Ferligoj, and Patrick Doreian

2.1 Introduction 11

2.2 Data Collection and Cleaning 12

2.2.1 Most Cited/Citing Works 15

2.2.2 The Boundary Problem for Citation Networks 17

2.3 Analyses of the Citation Networks 19

2.3.1 Components 20

2.3.2 The CPM Path of the Main Citation Network 20

2.3.3 Key-Route Paths 20

2.3.4 Positioning Sets of Selected Works in a Citation Network 30

2.4 Link Islands in the Clustering Network Literature 35

2.4.1 Island 10: Community Detection and Blockmodeling 35

2.4.2 Island 7: Engineering Geology 36

2.4.3 Island 9: Geophysics 38

2.4.4 Island 2: Electromagnetic Fields and their Impact on Humans 38

2.4.5 Limitations and Extensions 40

2.5 Authors 41

2.5.1 Productivity Inside Research Groups 42

2.5.2 Collaboration 43

2.5.3 Citations Among Authors Contributing to the Network Partitioning Literature 45

2.5.4 Citations Among Journals 47

2.5.5 Bibliographic Coupling 50

2.5.6 Linking Through a Jaccard Network 58

2.6 Summary and Future Work 62

Acknowledgements 63

References 63

3 Clustering Approaches to Networks 65
Vladimir Batagelj

3.1 Introduction 65

3.2 Clustering 66

3.2.1 The Clustering Problem 66

3.2.2 Criterion Functions 67

3.2.3 Cluster-Error Function/Examples 72

3.2.4 The Complexity of the Clustering Problem 75

3.3 Approaches to Clustering 76

3.3.1 Local Optimization 76

3.3.2 Dynamic Programming 79

3.3.3 Hierarchical Methods 79

3.3.4 Adding Hierarchical Methods 83

3.3.5 The Leaders Method 84

3.4 Clustering Graphs and Networks 87

3.5 Clustering in Graphs and Networks 89

3.5.1 An Indirect Approach 89

3.5.2 A Direct Approach: Blockmodeling 90

3.5.3 Graph Theoretic Approaches 90

3.6 Agglomerative Method for Relational Constraints 90

3.6.1 Software Support 95

3.7 Some Examples 95

3.7.1 The US Geographical Data, 2016 95

3.7.2 Citations Among Authors from the Network Clustering Literature 98

3.8 Conclusion 102

Acknowledgements 102

References 102

4 Different Approaches to Community Detection 105
Martin Rosvall, Jean-Charles Delvenne, Michael T. Schaub, and Renaud Lambiotte

4.1 Introduction 105

4.2 Minimizing Constraint Violations: the Cut-based Perspective 107

4.3 Maximizing Internal Density: the Clustering Perspective 108

4.4 Identifying Structural Equivalence: the Stochastic Block Model Perspective 110

4.5 Identifying Coarse-grained Descriptions: the Dynamical Perspective 111

4.6 Discussion 114

4.7 Conclusions 116

Acknowledgements 116

References 116

5 Label Propagation for Clustering 121
Lovro Šubelj

5.1 Label Propagation Method 121

5.1.1 Resolution of Label Ties 123

5.1.2 Order of Label Propagation 123

5.1.3 Label Equilibrium Criterium 124

5.1.4 Algorithm and Complexity 125

5.2 Label Propagation as Optimization 127

5.3 Advances of Label Propagation 128

5.3.1 Label Propagation Under Constraints 129

5.3.2 Label Propagation with Preferences 130

5.3.3 Method Stability and Complexity 133

5.4 Extensions to Other Networks 137

5.5 Alternative Types of Network Structures 139

5.5.1 Overlapping Groups of Nodes 139

5.5.2 Hierarchy of Groups of Nodes 140

5.5.3 Structural Equivalence Groups 142

5.6 Applications of Label Propagation 146

5.7 Summary and Outlook 146

References 147

6 Blockmodeling of Valued Networks 151
Carl Nordlund and Aleš Žiberna

6.1 Introduction 151

6.2 Valued Data Types 153

6.3 Transformations 154

6.3.1 Scaling Transformations 155

6.3.2 Dichotomization 157

6.3.3 Normalization Procedures 157

6.3.4 Iterative Row-column Normalization 158

6.3.5 Transaction-flow and Deviational Transformations 159

6.4 Indirect Clustering Approaches 160

6.4.1 Structural Equivalence: Indirect Metrics 160

6.4.2 The CONCOR Algorithm 161

6.4.3 Deviational Structural Equivalence: Indirect Approach 162

6.4.4 Regular Equivalence: The REGE Algorithms 162

6.4.5 Indirect Approaches: Finding Clusters, Interpreting Blocks 163

6.5 Direct Approaches 164

6.5.1 Generalized Blockmodeling 164

6.5.2 Generalized Blockmodeling of Valued Networks 165

6.5.3 Deviational Generalized Blockmodeling 166

6.6 On the Selection of Suitable Approaches 167

6.7 Examples 168

6.7.1 EIES Friendship Data at Time 2 168

6.7.2 Commodity Trade Within EU/EFTA 2010 173

6.8 Conclusion 183

Acknowledgements 185

References 185

7 Treating Missing Network Data Before Partitioning 189
Anja Žnidaršič, Patrick Doreian, and Anuška Ferligoj

7.1 Introduction 189

7.2 Types of Missing Network Data 190

7.2.1 Measurement Errors in Recorded (Or Reported) Ties 190

7.2.2 Item Non-Response 192

7.2.3 Actor Non-Response 192

7.3 Treatments of Missing Data (Due to Actor Non-Response) 193

7.3.1 Reconstruction 194

7.3.2 Imputations of the Mean Values of Incoming Ties 196

7.3.3 Imputations of the Modal Values of Incoming Ties 196

7.3.4 Reconstruction and Imputations Based on Modal Values of Incoming Ties 197

7.3.5 Imputations of the Total Mean 197

7.3.6 Imputations of Median of the Three Nearest Neighbors based on Incoming Ties 197

7.3.7 Null Tie Imputations 198

7.3.8 Blockmodel Results for the Whole and Treated Networks 198

7.4 A Study Design Examining the Impact of Non-Response Treatments on Clustering Results 200

7.4.1 Some Features of Indirect and Direct Blockmodeling 200

7.4.2 Design of the Simulation Study 201

7.4.3 The Real Networks Used in the Simulation Studies 201

7.5 Results 202

7.5.1 Indirect Blockmodeling of Real Valued Networks 202

7.5.2 Indirect Blockmodeling on Real Binary Networks 210

7.5.3 Direct Blockmodeling of Binary Real Networks 216

7.6 Conclusions 222

Acknowledgements 223

References 223

8 Partitioning Signed Networks 225
Vincent Traag, Patrick Doreian, and Andrej Mrvar

8.1 Notation 225

8.2 Structural Balance Theory 226

8.2.1 Weak Structural Balance 230

8.3 Partitioning 232

8.3.1 Strong Structural Balance 233

8.3.2 Weak Structural Balance 237

8.3.3 Blockmodeling 238

8.3.4 Community Detection 239

8.4 Empirical Analysis 242

8.5 Summary and Future Work 247

References 248

9 Partitioning Multimode Networks 251
Martin G Everett and Stephen P Borgatti

9.1 Introduction 251

9.2 Two-Mode Partitioning 252

9.3 Community Detection 253

9.4 Dual Projection 254

9.5 Signed Two-Mode Networks 257

9.6 Spectral Methods 258

9.7 Clustering 261

9.8 More Complex Data 262

9.9 Conclusion 263

References 263

10 Blockmodeling Linked Networks 267
Aleš Žiberna

10.1 Introduction 267

10.2 Blockmodeling Linked Networks 268

10.2.1 Separate Analysis 269

10.2.2 A True Linked Blockmodeling Approach 269

10.2.3 Weighting of Different Parts of a Linked Network 270

10.3 Examples 270

10.3.1 Co-authorship Network at Two Time-points 270

10.3.2 A Multilevel Network of Participants at a Trade Fair for TV Programs 277

10.4 Conclusion 284

Acknowledgements 285

References 285

11 Bayesian Stochastic Blockmodeling 289
Tiago P. Peixoto

11.1 Introduction 289

11.2 Structure Versus Randomness in Networks 290

11.3 The Stochastic Blockmodel 292

11.4 Bayesian Inference: The Posterior Probability of Partitions 294

11.5 Microcanonical Models and the Minimum Description Length Principle 298

11.6 The “Resolution Limit” Underfitting Problem and the Nested SBM 300

11.7 Model Variations 305

11.7.1 Model Selection 306

11.7.2 Degree Correction 306

11.7.3 Group Overlaps 310

11.7.4 Further Model Extensions 313

11.8 Efficient Inference Using Markov Chain Monte Carlo 314

11.9 To Sample or To Optimize? 317

11.10 Generalization and Prediction 321

11.11 Fundamental Limits of Inference: The Detectability–Indetectability Phase Transition 323

11.12 Conclusion 327

References 328

12 Structured Networks and Coarse-Grained Descriptions: A Dynamical Perspective 333
Michael T. Schaub, Jean-Charles Delvenne, Renaud Lambiotte, and Mauricio Barahona

12.1 Introduction 333

12.2 Part I: Dynamics on and of Networks 337

12.2.1 General Setup 337

12.2.2 Consensus Dynamics 338

12.2.3 Diffusion Processes and Random Walks 340

12.3 Part II: The Influence of Graph Structure on Network Dynamics 342

12.3.1 Time Scale Separation in Partitioned Networks 342

12.3.2 Strictly Invariant Subspaces of the Network Dynamics and External Equitable Partitions 345

12.3.3 Structural Balance: Consensus on Signed Networks and Polarized Opinion Dynamics 348

12.4 Part III: Using Dynamical Processes to Reveal Network Structure 351

12.4.1 A Generic Algorithmic Framework for Dynamics-Based Network Partitioning and Coarse Graining 352

12.4.2 Extending the Framework by using other Measures 354

12.5 Discussion 357

Acknowledgements 358

References 358

13 Scientific Co-Authorship Networks 363
Marjan Cugmas, Anuška Ferligoj, and Luka Kronegger

13.1 Introduction 363

13.2 Methods 364

13.2.1 Blockmodeling 365

13.2.2 Measuring the Obtained Blockmodels’ Stability 365

13.3 The Data 369

13.4 The Structure of Obtained Blockmodels 370

13.5 Stability of the Obtained Blockmodel Structures 378

13.5.1 Clustering of Scientific Disciplines According to Different Operationalizations of Core Stability 378

13.5.2 Explaining the Stability of Cores 382

13.6 Conclusions 384

Acknowledgements 386

References 386

14 Conclusions and Directions for Future Work 389
Patrick Doreian, Anuška Ferligoj, and Vladimir Batagelj

14.1 Issues Raised within Chapters 390

14.2 Linking Ideas Found in Different Chapters 395

14.3 A Brief Summary and Conclusion 397

References 397

Topic Index 399

Person Index 407

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Patrick Doreian Department of Sociology, University of Pittsburgh, USA and Faculty of Social Sciences, University of Ljubljana, Slovenia.

Vladimir Batagelj Department of Mathematics, Faculty of Mathematics and Physics, University of Ljubljana, Slovenia.

Anuska Ferligoj Faculty of Social Sciences, University of Ljubljana, Slove.
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