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E-raamat: Advances in Network Clustering and Blockmodeling [Wiley Online]

Edited by (Department of Sociology, University of Pittsburgh, USA and Faculty of Social Sciences, University of Ljubljana, Slovenia), Edited by (Department of Mathematics, Faculty of Mathematics and Physics, University of Ljubljana, Slovenia), Edited by (Faculty of)
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Advances in Network Clustering and BlockmodelingSuurem pilt
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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.

List of Contributors
xv
1 Introduction
1(10)
Patrick Doreian
Vladimir Batagelj
Anuska Ferligoj
1.1 On the
Chapters
1(8)
1.2 Looking Forward
9(2)
2 Bibliometric Analyses of the Network Clustering Literature
11(54)
Vladimir Batagelj
Anuska Ferligoj
Patrick Doreian
2.1 Introduction
11(1)
2.2 Data Collection and Cleaning
12(7)
2.2.1 Most Cited/Citing Works
15(2)
2.2.2 The Boundary Problem for Citation Networks
17(2)
2.3 Analyses of the Citation Networks
19(16)
2.3.1 Components
20(1)
2.3.2 The CPM Path of the Main Citation Network
20(1)
2.3.3 Key-Route Paths
20(10)
2.3.4 Positioning Sets of Selected Works in a Citation Network
30(5)
2.4 Link Islands in the Clustering Network Literature
35(6)
2.4.1 Island 10: Community Detection and Blockmodeling
35(1)
2.4.2 Island 7: Engineering Geology
36(2)
2.4.3 Island 9: Geophysics
38(1)
2.4.4 Island 2: Electromagnetic Fields and their Impact on Humans
38(2)
2.4.5 Limitations and Extensions
40(1)
2.5 Authors
41(21)
2.5.1 Productivity Inside Research Groups
42(1)
2.5.2 Collaboration
43(2)
2.5.3 Citations Among Authors Contributing to the Network Partitioning Literature
45(2)
2.5.4 Citations Among Journals
47(3)
2.5.5 Bibliographic Coupling
50(8)
2.5.6 Linking Through a Jaccard Network
58(4)
2.6 Summary and Future Work
62(3)
Acknowledgements
63(1)
References
63(2)
3 Clustering Approaches to Networks
65(40)
Vladimir Batagelj
3.1 Introduction
65(1)
3.2 Clustering
66(10)
3.2.1 The Clustering Problem
66(1)
3.2.2 Criterion Functions
67(5)
3.2.3 Cluster-Error Function/Examples
72(3)
3.2.4 The Complexity of the Clustering Problem
75(1)
3.3 Approaches to Clustering
76(11)
3.3.7 Local Optimization
76(3)
3.3.2 Dynamic Programming
79(1)
3.3.3 Hierarchical Methods
79(4)
3.3.4 Adding Hierarchical Methods
83(1)
3.3.5 The Leaders Method
84(3)
3.4 Clustering Graphs and Networks
87(2)
3.5 Clustering in Graphs and Networks
89(1)
3.5.1 An Indirect Approach
89(1)
3.5.2 A Direct Approach: Blockmodeling
90(1)
3.5.3 Graph Theoretic Approaches
90(1)
3.6 Agglomerative Method for Relational Constraints
90(5)
3.6.1 Software Support
95(1)
3.7 Some Examples
95(7)
3.7.1 The US Geographical Data, 2016
95(3)
3.7.2 Citations Among Authors from the Network Clustering Literature
98(4)
3.8 Conclusion
102(3)
Acknowledgements
102(1)
References
102(3)
4 Different Approaches to Community Detection
105(16)
Martin Rosvall
Jean-Charles Delvenne
Michael T. Schaub
Renaud Lambiotte
4.1 Introduction
105(2)
4.2 Minimizing Constraint Violations: the Cut-based Perspective
107(1)
4.3 Maximizing Internal Density: the Clustering Perspective
108(2)
4.4 Identifying Structural Equivalence: the Stochastic Block Model Perspective
110(1)
4.5 Identifying Coarse-grained Descriptions: the Dynamical Perspective
111(3)
4.6 Discussion
114(2)
4.7 Conclusions
116(5)
Acknowledgements
116(1)
References
116(5)
5 Label Propagation for Clustering
121(30)
Lovro Subelj
5.1 Label Propagation Method
121(6)
5.1.1 Resolution of Label Ties
123(1)
5.1.2 Order of Label Propagation
123(1)
5.1.3 Label Equilibrium Criterium
124(1)
5.1.4 Algorithm and Complexity
125(2)
5.2 Label Propagation as Optimization
127(1)
5.3 Advances of Label Propagation
128(9)
5.3.1 Label Propagation Under Constraints
129(1)
5.3.2 Label Propagation with Preferences
130(3)
5.3.3 Method Stability and Complexity
133(4)
5.4 Extensions to Other Networks
137(2)
5.5 Alternative Types of Network Structures
139(7)
5.5.1 Overlapping Groups of Nodes
139(1)
5.5.2 Hierarchy of Groups of Nodes
140(2)
5.5.3 Structural Equivalence Groups
142(4)
5.6 Applications of Label Propagation
146(1)
5.7 Summary and Outlook
146(5)
References
147(4)
6 Blockmodeling of Valued Networks
151(38)
Carl Nordlund
Ales Ziberna
6.1 Introduction
151(2)
6.2 Valued Data Types
153(1)
6.3 Transformations
154(6)
6.3.1 Scaling Transformations
155(2)
6.3.2 Dichotomization
157(1)
6.3.3 Normalization Procedures
157(1)
6.3.4 Iterative Row-column Normalization
158(1)
6.3.5 Transaction-flow and Deviational Transformations
159(1)
6.4 Indirect Clustering Approaches
160(4)
6.4.1 Structural Equivalence: Indirect Metrics
160(1)
6.4.2 The CON COR A Igorithm
161(1)
6.4.3 Deviational Structural Equivalence: Indirect Approach
162(1)
6.4.4 Regular Equivalence: The REGE Algorithms
162(1)
6.4.5 Indirect Approaches: Finding Clusters, Interpreting Blocks
163(1)
6.5 Direct Approaches
164(3)
6.5.1 Generalized Blockmodeling
164(1)
6.5.2 Generalized Blockmodeling of Valued Networks
165(1)
6.5.3 Deviational Generalized Blockmodeling
166(1)
6.6 On the Selection of Suitable Approaches
167(1)
6.7 Examples
168(15)
6.7.1 EIES Friendship Data at Time 2
168(5)
6.7.2 Commodity Trade Within EU/EFTA 2010
173(10)
6.8 Conclusion
183(6)
Acknowledgements
185(1)
References
185(4)
7 Treating Missing Network Data Before Partitioning
189(36)
Anja Znidarsic
Patrick Doreian
Anuska Ferligoj
7.1 Introduction
189(1)
7.2 Types of Missing Network Data
190(3)
7.2.1 Measurement Errors in Recorded (Or Reported) Ties
190(2)
7.2.2 Item Non-Response
192(1)
7.2.3 Actor Non-Response
192(1)
7.3 Treatments of Missing Data (Due to Actor Non-Response)
193(7)
7.3.1 Reconstruction
194(2)
7.3.2 Imputations of the Mean Values of Incoming Ties
196(1)
7.3.3 Imputations of the Modal Values of Incoming Ties
196(1)
7.3.4 Reconstruction and Imputations Based on Modal Values of Incoming Ties
197(1)
7.3.5 Imputations of the Total Mean
197(1)
7.3.6 Imputations of Median of the Three Nearest Neighbors based on Incoming Ties
197(1)
7.3.7 Null Tie Imputations
198(1)
7.3.8 Blockmodel Results for the Whole and Treated Networks
198(2)
7.4 A Study Design Examining the Impact of Non-Response Treatments on Clustering Results
200(2)
7.4.1 Some Features of Indirect and Direct Blockmodeling
200(1)
7.4.2 Design of the Simulation Study
201(1)
7.4.3 The Real Networks Used in the Simulation Studies
201(1)
7.5 Results
202(20)
7.5.1 Indirect Blockmodeling of Real Valued Networks
202(8)
7.5.2 Indirect Blockmodeling on Real Binary Networks
210(6)
7.5.3 Direct Blockmodeling of Binary Real Networks
216(6)
7.6 Conclusions
222(3)
Acknowledgements
223(1)
References
223(2)
8 Partitioning Signed Networks
225(26)
Vincent Traag
Patrick Doreian
Andre] Mrvar
8.1 Notation
225(1)
8.2 Structural Balance Theory
226(6)
8.2.1 Weak Structural Balance
230(2)
8.3 Partitioning
232(10)
8.3.1 Strong Structural Balance
233(4)
8.3.2 Weak Structural Balance
237(1)
8.3.3 Blockmodeling
238(1)
8.3.4 Community Detection
239(3)
8.4 Empirical Analysis
242(5)
8.5 Summary and Future Work
247(4)
References
248(3)
9 Partitioning Multimode Networks
251(16)
Martin G. Everett
Stephen P. Borgatti
9.1 Introduction
251(1)
9.2 Two-Mode Partitioning
252(1)
9.3 Community Detection
253(1)
9.4 Dual Projection
254(3)
9.5 Signed Two-Mode Networks
257(1)
9.6 Spectral Methods
258(3)
9.7 Clustering
261(1)
9.8 More Complex Data
262(1)
9.9 Conclusion
263(4)
References
263(4)
10 Blockmodeling Linked Networks
267(22)
Ales Ziberna
10.1 Introduction
267(1)
10.2 Blockmodeling Linked Networks
268(2)
10.2.1 Separate Analysis
269(1)
10.2.2 A True Linked Blockmodeling Approach
269(1)
10.2.3 Weighting of Different Parts of a Linked Network
270(1)
10.3 Examples
270(14)
10.3.1 Co-authorship Network at Two Time-points
270(7)
10.3.2 A Multilevel Network of Participants at a Trade Fair for TV Programs
277(7)
10.4 Conclusion
284(5)
Acknowledgements
285(1)
References
285(4)
11 Bayesian Stochastic Blockmodeling
289(44)
Tiago P. Peixoto
11.1 Introduction
289(1)
11.2 Structure Versus Randomness in Networks
290(2)
11.3 The Stochastic Blockmodel
292(2)
11.4 Bayesian Inference: The Posterior Probability of Partitions
294(4)
11.5 Microcanonical Models and the Minimum Description Length Principle
298(2)
11.6 The "Resolution Limit" Underfitting Problem and the Nested SBM
300(5)
11.7 Model Variations
305(9)
11.7.1 Model Selection
306(1)
11.7.2 Degree Correction
306(4)
11.7.3 Group Overlaps
310(3)
11.7.4 Further Model Extensions
313(1)
11.8 Efficient Inference Using Markov Chain Monte Carlo
314(3)
11.9 To Sample or To Optimize?
317(4)
11.10 Generalization and Prediction
321(2)
11.11 Fundamental Limits of Inference: The Detectabilily--Indetectability Phase Transition
323(4)
11.12 Conclusion
327(6)
References
328(5)
12 Structured Networks and Coarse-Grained Descriptions: A Dynamical Perspective
333(30)
Michael T. Schaub
Jean-Charles Delvenne
Renaud Lambiotte
Mauricio Barahona
12.1 Introduction
333(4)
12.2 Part I: Dynamics on and of Networks
337(5)
12.2.1 General Setup
337(1)
12.2.2 Consensus Dynamics
338(2)
12.2.3 Diffusion Processes and Random Walks
340(2)
12.3 Part II: The Influence of Graph Structure on Network Dynamics
342(9)
12.3.1 Time Scale Separation in Partitioned Networks
342(1)
12.3.2 Strictly Invariant Subspaces of the Network Dynamics and External Equitable Partitions
343(5)
12.3.3 Structural Balance: Consensus on Signed Networks and Polarized Opinion Dynamics
348(3)
12.4 Part III: Using Dynamical Processes to Reveal Network Structure
351(6)
12.4.1 A Generic Algorithmic Framework for Dynamics-Based Network Partitioning and Coarse Graining
352(2)
12.4.2 Extending the Framework by using other Measures
354(3)
12.5 Discussion
357(6)
Acknowledgements
358(1)
References
358(5)
13 Scientific Co-Authorship Networks
363(26)
Marjan Cugmas
Anuska Ferligoj
Luka Kronegger
13.1 Introduction
353(11)
13.2 Methods
364(5)
13.2.1 Blockmodeling
265(100)
13.2.2 Measuring the Obtained Blockmodels' Stability
365(4)
13.3 The Data
369(1)
13.4 The Structure of Obtained Blockmodels
370(8)
13.5 Stability of the Obtained Blockmodel Structures
378(6)
13.5.1 Clustering of Scientific Disciplines According to Different Operationalizations of Core Stability
378(4)
13.5.2 Explaining the Stability of Cores
382(2)
13.6 Conclusions
384(5)
Acknowledgements
386(1)
References
386(3)
14 Conclusions and Directions for Future Work
389(10)
Patrick Doreian
Anuska Ferligoj
Vladimir Batagelj
14.1 Issues Raised within
Chapters
390(5)
14.2 Linking Ideas Found in Different
Chapters
395(2)
14.3 A Brief Summary and Conclusion
397(2)
References
397(2)
Topic Index 399(8)
Person Index 407
Patrick Doreian, MA, is Professor Emeritus of Sociology and Statistics at the University of Pittsburgh and has a research position at the Faculty of Social Sciences at the University of Ljubljana. He has published over 150 articles in academic journals as well as nine books and numerous book chapters. His co-authored book Generalized Blockmodeling written with Vladimir Batagelj and Anuka Ferligoj received the Harrison White Outstanding Book Award in 2007. He is an honorary Senator of the University of Ljubljana, Slovenia.

Vladimir Batagelj, PhD, is Professor Emeritus of Discrete and Computational Mathematics from the University of Ljubljana, Slovenia. He is Senior Researcher at the Department of Theoretical Computer Science of IMFM, Ljubljana, the Institute Andrej Maruic at University of Primorska, Koper, and NRU HSE International Laboratory for Applied Network Research, Moscow. He is a co-author of program Pajek for large network analysis and visualization. He is an elected member of the International Statistical Institute. With Patrick Doreian, Anuka Ferligoj and Nataa Kej??ar he co-authored the book Understanding Large Temporal Networks and Spatial Networks, Wiley, 2014.

Anuka Ferligoj, PhD, is Professor of Statistics at the Faculty of Social Sciences at the University of Ljubljana and academic supervisor at the NRU HSE International Laboratory for Applied Network Research, Moscow. She is a member of the European Academy of Sociology. In 2010 she received the Doctor et Professor Honoris Causa at the Eötvös Loránd University, Budapest, Hungary.
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