Social Network Analysis; Methods and Applications

Stanley Wasserman and Katherine Faust

**CAMBRIDGE **UNIVERSITY PRESS

ISBN-10: 0521387078 | ISBN-13: 978-0521387071 |

Publication Date: November 25, 1994 | Edition: 1

In this post I wanted to introduce one of leading handbooks in Social Networks field titled as Social Network Analysis; Methods and Applications; in this books’ page in Amazon it has been introduced by these words:

“**Book Description:**

Social network analysis, which focuses on relationships among social entities, is used widely in the social and behavioral sciences, as well as in economics, marketing, and industrial engineering. Social Network Analysis: Methods and Applications reviews and discusses methods for the analysis of social networks with a focus on applications of these methods to many substantive examples. As the first book to provide a comprehensive coverage of the methodology and applications of the field, this study is both a reference book and a textbook.”

.

Here I have written this book’s contents list, in near future I will write here what I have reached by reading this book and I will describe this book’s parts and chapters separately.

You can find a Persian description of this book here.

**Contents**

**Part I: Networks, Relations, and Structure**

1 Social Network Analysis in the Social and Behavioral Sciences 3

1.1 The Social Networks Perspective 4

1.2 Historical and Theoretical Foundations 10

1.2.1 Empirical Motivations 11

1.2,2 Theoretical Motivations 13

1.2.3 Mathematical Motivations 15

1.2.4 In Summary 16

1.3 Fundamental Concepts in Network Analysis 17

1.4 Distinctive Features 21

1.5 Organization of the Book and How to Read It 22

1.5.1 Complexity 23

1.5.2 DeSCriptive and Statistical Methods 23

1.5.3 Theory Driven Methods 24

1.5.4 Chronology 24

1.5.5 Levels of Analysis 25

1.5.6 Chapter Prerequisites 26

1.6 Summary 27

2 Social Network Data 28

2.1 Introduction: What Are Network Data? 28

2.1.1 Structural and Composition Variables 29

2.1.2 Modes 29

2.1.3 Affiliation Variables 30

2.2 Boundary Specification and Sampling 30

2.2.1 What Is Your Population? 31

2.2.2 Sampling 33

2.3 Types of Networks 35

2.3.1 One-Mode Networks 36

2.3.2 Two-Mode Networks 39

2.3.3 Ego-centered and Special Dyadic Networks 41

2.4 Network Data, Measurement and Collection 43

2.4.1 Measurement 43

2.4.2 Collection 45

2.4.3 Longitudinal Data Collection 55

2.4.4 Measurement Validity, Reliability, Accuracy, Error 56

2.5 Data Sets Found in These Pages 59

2.5.1 Krackhardt’s High-tech Managers 60

2.5.2 Padgett’s Florentine Families 61

2.5.3 Freeman’s EIES Network 62

2.5.4 Countries Trade Data 64

2.5.5 Galaskiewicz’s CEOs and Clubs Network 65

2.5.6 Other Data 66

**Part II: Mathematical Representations of Social Networks 67**

3 Notation for Social Network Data 69

3.1 Graph Theoretic Notation 71

3.1.1 A Single Relation 71

3.1.2 OMultiple Relations 73

3.1.3 Summary 75

3.2 Sociometric Notation 77

3.2.1 Single Relation 79

3.2.2 Multiple Relations 81

3.2.3 Summary 83

3.3 OAlgebraic Notation 84

3.4 OTwo Sets of Actors 85

3.4.1 (8)Different Types of Pairs 86

3.4.2 OSociometric Notation 87

3.5 Putting It All Together 89

4 Graphs and Matrices 92

4.1 Why Graphs? 93

4.2 Graphs 94

4.2.1 Subgraphs, Dyads, and Triads 97

4.2.2 Nodal Degree 100

4.2.3 Density of Graphs and Subgraphs 101

4.2.4 Example: Padgett’s Florentine Families 103

4.2.5 Walks, Trails, and Paths 105

4.2.6 Connected Graphs and Components 109

4.2.7 Geodesics, Distance, and Diameter 110

4.2.8 Connectivity of Graphs 112

4.2.9 Isomorphic Graphs and Subgraphs 117

4.2.10 OSpecial Kinds of Graphs 119

4.3 Directed Graphs 121

4.3.1 Subgraphs – Dyads 124

4.3.2 Nodal Indegree and Outdegree 125

4.3.3 Density of a Directed Graph 129

4.3.4 An Example 129

4.3.5 Directed Walks, Paths, Semipaths 129

4.3.6 Reachability and Connectivity in Digraphs 132

4.3.7 Geodesics, Distance and Diameter 134

4.3.8 OSpecial Kinds of Directed Graphs 134

4.3.9 Summary 136

4.4 Signed Graphs and Signed Directed Graphs 136

4.4.1 Signed Graph 137

4.4.2 Signed Directed Graphs 138

4.5 Valued Graphs and Valued Directed Graphs 140

4.5.1 Nodes and Dyads 142

4.5.2 Density in a Valued Graph 143

4.5.3 OPaths in Valued Graphs 143

4.6 Multigraphs 145

4.7 (8)Hypergraphs 146

4.8 Relations 148

4.8.1 Definition 148

4.8.2 Properties of Relations 149

4.9 Matrices 150

4.9.1 Matrices for Graphs 150

4.9.2 Matrices for Digraphs 152

4.9.3 Matrices for Valued Graphs 153

4.9.4 Matrices for Two-Mode Networks 154

4.9.5 OMatrices for Hypergraphs 154

4.9.6 Basic Matrix Operations 154

4.9.7 Computing Simple Network Properties 159

4.9.8 Summary 164

4.10 Properties 164

4.10.1 Reflexivity 164

4.10.2 Symmetry 165

4.10.3 Transitivity 165

4.11 Summary 165

**Part III: Structural and Locational Properties 167**

5 Centrality and Prestige 169

5.1 Prominence: Centrality and Prestige 172

5.1.1 Actor Centrality 173

5.1.2 Actor Prestige 174

5.1.3 Group Centralization and Group Prestige 175

5.2 Nondirectional Relations 177

5.2.1 Degree Centrality 178

5.2.2 Closeness Centrality

5.2.3 Betweenness Centrality

5.2.4 (8)Information Centrality

5.3 Directional Relations

5.3.1 Centrality

5.3.2 Prestige

5.3.3 A Different Example

5.4 Comparisons and Extensions

6 Strnctural Balance and Transitivity

6.1 Structural Balance

6.1.1 Signed Nondirectional Relations

6.1.2 Signed Directional Relations

6.1.3 OChecking for Balance

6.1.4 An Index for Balance

6.1.5 Summary

6.2 Clusterability

6.2.1 The Clustering Theorems

6.2.2 Summary

6.3 Generalizations of Clusterability

6.3.1 Empirical Evidence 239

6.3.2 ORanked Clusterability 240

6.3.3 Summary 242

6.4 Transitivity 243

6.5 Conclusion 247

7 Cohesive Subgroups 249

7.1 Background 250

7.1.1 Social Group and Subgroup 250

7.1.2 Notation 252

7.2 Subgroups Based on Complete Mutuality 253

7.2.1 Definition of a Clique 254

7.2.2 An Example 254

7.2.3 Considerations 256

7.3 Reachability and Diameter 257

7.3.1 n-cliques 258

7.3.2 An Example 259

7.3.3 Considerations 260

7.3.4 n-clans and n-clubs 260

7.3.5 Summary 262

7.4 Subgroups Based on Nodal Degree 263

7.4.1 k-plexes 265

7.4.2 k-cores 266

7.5 Comparing Within to Outside Subgroup Ties 267

7.5.1 LS Sets 268

7.5.2 Lambda Sets 269

7.6 Measures of Subgroup Cohesion 270

7.7 Directional Relations 273

7.7.1 Cliques Based on Reciprocated Ties 273

7.7.2 Connectivity in Directional Relations 274

7.7.3 n-cliques in Directional Relations 275

7.8 Valued Relations 277

7.8.1 Cliques, n-cliques, and k-plexes 278

7.8.2 Other Approaches for Valued Relations 282

7.9 Interpretation of Cohesive Subgroups 283

7.10 Other Approaches 284

7.10.1 Matrix Permutation Approaches 284

7.10.2 Multidimensional Scaling 287

7.10.3 OFactor Analysis 290

7.11 Summary 290

8 Affiliations and Overlapping Snbgroups 291

8.1 Affiliation Networks 291

8.2 Background 292

8.2.1 Theory 292

8.2.2 Concepts 294

8.2.3 Applications and Rationale 295

8.3 Representing Affiliation Networks 298

8.3.1 The Affiliation Network Matrix 298

8.3.2 Bipartite Graph 299

8.3.3 Hypergraph 303

8.3.4 OSimplices and Simplicial Complexes 306

8.3.5 Summary 306

8.3.6 An example: Galaskiewicz’s CEOs and Clubs 307

8.4 One-mode Networks 307

8.4.1 Definition 307

8.4.2 Examples 309

8.5 Properties of Affiliation Networks 312

8.5.1 Properties of Actors and Events 312

8.5.2 Properties of One-mode Networks 314

8.5.3 Taking Account of Subgroup Size 322

8.5.4 Interpretation 324

8.6 (8)Analysis of Actors and Events 326

8.6.1 (8)Galois Lattices 326

8.6.2 (8)Correspondence Analysis 334

8.7 Summary 342

**Part IV: Roles and Positions 345**

9 Strnctural Eqnivalence 347

9.1 Background 348

9.1.1 Social Roles and Positions 348

9.1.2 An Overview of Positional and Role Analysis 351

9.1.3 A Brief History 354

9.2 Definition of Structural Equivalence 356

9.2.1 Definition 356

9.2.2 An Example 357

9.2.3 Some Issues in Defining Structural Equivalence 359

9.3 Positional Analysis 361

9.3.1 Simplification of Multirelational Networks 361

9.3.2 Tasks in a Positional Analysis 363

9.4 Measuring Structural Equivalence 366

9.4.1 Euclidean Distance as a Measure of Structural

Equivalence 367

9.4.2 Correlation as a Measure of Structural Equivalence 368

9.4.3 Some Considerations in Measuring Structural

Equivalence 370

9.5 Representation of Network Positions 375

9.5.1 Partitioning Actors 375

9.5.2 Spatial Representations of Actor Equivalences 385

9.5.3 Ties Between and Within Positions 388

9.6 Summary 391

10 Blockmodels

10.1 Definition

10.2 Building Blocks

10.2.1 Perfect Fit (Fat Fit)

10.2.2 Zeroblock (Lean Fit) Criterion

10.2.3 Oneblock Criterion

10.2.4 ct Density Criterion

10.2.5 Comparison of Criteria

10.2.6 Examples

10.2.7 Valued Relations

10.3 Interpretation

10.3.1 Actor Attributes

10.3.2 Describing Individual Positions

10.3.3 Image Matrices

10.4 Summary

11 Relational Algebras 425

11.1 Background 426

11.2 Notation and Algebraic Operations 428

11.2.1 Composition and Compound Relations 429

11.2.2 Properties of Composition and Compound

Relations 432

11.3 Multiplication Tables for Relations 433

11.3.1 Multiplication Tables and Relational Structures 435

11.3.2 An Example 439

11.4 Simplification of Role Tables 442

11.4.1 Simplification by Comparing Images 443

11.4.2 (8)Homomorphic Reduction 445

11.5 (8)Comparing Role Structures 449

11.5.1 Joint Homomorphic Reduction 451

11.5.2 The Common Structure Semigroup 452

11.5.3 An Example 453

11.5.4 Measuring the Similarity of Role Structures 457

11.6 Summary 460

12 Network Positions and Roles 461

12.1 Background 462

12.1.1 Theoretical Definitions of Roles and Positions 462

12.1.2 Levels of Role Analysis in Social Networks 464

12.1.3 Equivalences in Networks 466

12.2 Structural Equivalence, Revisited 468

12.3 Automorphic and Isomorphic Equivalence 469

12.3.1 Definition 470

12.3.2 Example 471

12.3.3 Measuring Automorphic Equivalence 472

12.4 Regular Equivalence 473

12.4.1 Definition of Regular Equivalence 474

12.4.2 Regular Equivalence for Nondirectional Relations 475

12.4.3 Regular Equivalence Blockmodels 476

12.4.4 OA Measure of Regular Equivalence 479

12.4.5 An Example 481

12.5 “Types” of Ties 483

12.5.1 An Example 485

12.6 Local Role Equivalence 487

12.6.1 Measuring Local Role Dissimilarity 488

12.6.2 Examples 491

12.7 (8)Ego Algebras 494

12.7.1 Definition of Ego Algebras 496

12.7.2 Equivalence of Ego Algebras 497

12.7.3 Measuring Ego Algebra Similarity 497

12.7.4 Examples 499

12.8 Discussion 502

**Part V: Dyadic and Triadic Methods**

13 Dyads

13.1 An Overview

13.2 An Example and Some Definitions

13.3 Dyads

13.3.1 The Dyad Census

13.3.2 The Example and Its Dyad Census

13.3.3 An Index for Mutuality

13.3.4 (8)A Second Index for Mutuality

13.3.5 OSubgraph Analysis, in General

13.4 Simple Distributions

13.4.1 The Uniform Distribution – A Review

13.4.2 Simple Distributions on Digraphs

13.5 Statistical Analysis of the Number of Arcs

13.5.1 Testing

13.5.2 Estimation

13.6 (8)Conditional Uniform Distributions 535

13.6.1 Uniform Distribution, Conditional on the Number

of Arcs 536

13.6.2 Uniform Distribution, Conditional on the

Outdegrees

13.7 Statistical Analysis of the Number of Mutuals

13.7.1 Estimation

13.7.2 Testing 542

13.7.3 Examples 543

13.8 (8)Other Conditional Uniform Distributions 544

13.8.1 Uniform Distribution, Conditional on the Indegrees 545

13.8.2 The UlMAN Distribution 547

13.8.3 More Complex Distributions 550

13.9 Other Research 552

13.10 Conclusion 555

14 Triads 556

14.1 Random Models and Substantive Hypotheses 558

14.2 Triads 559

14.2.1 The Triad Census 564

14.2.2 The Example and Its Triad Census 574

14.3 Distribution of a Triad Census 575

14.3.1 (8)Mean and Variance of a k-subgraph Census 576

14.3.2 Mean and Variance of a Triad Census 579

14.3.3 Return to the Example 581

14.3.4 Mean and Variance of Linear Combinations of a

Triad Census 582

14.3.5 A Brief Review 584

14.4 Testing Structural Hypotheses 585

14.4.1 Configurations 585

14.4.2 From Configurations to Weighting Vectors 590

14.4.3 From Weighting Vectors to Test Statistics 592

14.4.4 An Example 595

14.4.5 Another Example – Testing for Transitivity 596

14.5 Generalizations and Conclusions 598

14.6 Summary 601

**Part VI: Statistical Dyadic Interaction Models 603**

15 Statistical Analysis of Single Relational Networks 605

15.1 Single Directional Relations 607

15.1.1 The Y-array 608

15.1.2 Modeling the Y-array 612

15.1.3 Parameters 619

15.1.4 (8)Is PI a Random Directed Graph Distribution? 633

15.1.5 Summary 634

15.2 Attribute Variables 635

15.2.1 Introduction 636

15.2.2 The W-array 637

15.2.3 The Basic Model with Attribute Variables 640

15.2.4 Examples: Using Attribute Variables

15.3 Related Models for Further Aggregated Data

15.3.1 Strict Relational Analysis – The V-array

15.3.2 Ordinal Relational Data

15.4 ONondirectional Relations 656

15.4.1 A Model 656

15.4.2 An Example 657

15.5 (8)Recent Generalizations of PI 658

15.6 (8)Single Relations and Two Sets of Actors 662

15.6.1 Introduction 662

15.6.2 The Basic Model 663

15.6.3 Aggregating Dyads for Two-mode Networks 664

15.7 Computing for Log-linear Models

15.7.1 Computing Packages

15.7.2 From Printouts to Parameters

15.8 Summary

16 Stochastic Blockmodels and Goodness-of-Fit Indices

16.1 Evaluating Blockmodels

16.1.1 Goodness-of-Fit Statistics for Blockmodels

16.1.2 Structurally Based Blockmodels and Permutation

Tests 688

16.1.3 An Example 689

16.2 Stochastic Blockmodels 692

16.2.1 Definition of a Stochastic Blockmodel 694

16.2.2 Definition of Stochastic Equivalence 696

16.2.3 Application to Special Probability Functions 697

16.2.4 Goodness-of-Fit Indices for Stochastic Blockmodels 703

16.2.5 OStochastic a posteriori Blockmodels

16.2.6 Measures of Stochastic Equivalence

16.2.7 Stochastic Blockmodel Representations

16.2.8 The Example Continued

16.3 Summary: Generalizations and Extensions 719

16.3.1 Statistical Analysis of Multiple Relational Networks 719

16.3.2 Statistical Analysis of Longitudinal Relations 721

**Part VII: Epilogue 725**

17 Future Directions 727

17.1 Statistical Models 727

17.2 Generalizing to New Kinds of Data 729

17.2.1 Multiple Relations 730

17.2.2 Dynamic and Longitudinal Network Models 730

17.2.3 Ego-centered Networks 731

17.3 Data Collection 731

17.4 Sampling 732

17.5 General Propositions about Structure 732

17.6 Computer Technology 733

17.7 Networks and Standard Social and Behavioral Science 733

Appendix A Compoter Programs 735

Appendix B Data 738

References 756

Name Index 802

Subject Index 811

List of Notation 819

ISBN-10: 0521387078 | ISBN-13: 978-0521387071 | Publication Date: November 25, 1994 | Edition: 1