Social Network Analysis: Methods and Applications

, by Stanley Wasserman , Katherine Faust

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ISBN: 9780521387071 | 0521387078
Cover: Paperback
Copyright: 11/25/1994

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Social network analysis is used widely in the social and behavioral sciences, as well as in economics, marketing, and industrial engineering. The social network perspective focuses on relationships among social entities and is an important addition to standard social and behavioral research, which is primarily concerned with attributes of the social units. 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. It is a reference book that can be used by those who want a comprehensive review of network methods, or by researchers who have gathered network data and want to find the most appropriate method by which to analyze it. It is also intended for use as a textbook as it is the first book to provide comprehensive coverage of the methodology and applications of the field.

List of Tables

xxi

List of Illustrations

xxiv

Preface

xxix

Part I: Networks, Relations, and Structure

(66)

Social Network Analysis in the Social and Behavioral Sciences

(25)

The Social Networks Perspective

(6)

Historical and Theoretical Foundations

(7)

Empirical Motivations

(2)

Theoretical Motivations

(2)

Mathematical Motivations

(1)

In Summary

(1)

Fundamental Concepts in Network Analysis

(4)

Distinctive Features

(1)

Organization of the Book and How to Read It

(5)

Complexity

(1)

Descriptive and Statistical Methods

(1)

Theory Driven Methods

(1)

Chronology

(1)

Levels of Analysis

(1)

Chapter Prerequisites

(1)

Summary

(1)

Social Network Data

(39)

Introduction: What Are Network Data?

(2)

Structural and Composition Variables

(1)

Modes

(1)

Affiliation Variables

(1)

Boundary Specification and Sampling

(5)

What Is Your Population?

(2)

Sampling

(2)

Types of Networks

(8)

One-Mode Networks

(3)

Two-Mode Networks

(2)

Ego-centered and Special Dyadic Networks

(2)

Network Data, Measurement and Collection

(16)

Measurement

(2)

Collection

(10)

Longitudinal Data Collection

(1)

Measurement Validity, Reliability, Accuracy, Error

(3)

Data Sets Found in These Pages

(8)

Krackhardt's High-tech Managers

(1)

Padgett's Florentine Families

(1)

Freeman's EIES Network

(2)

Countries Trade Data

(1)

Galaskiewicz's CEOs and Clubs Network

(1)

Other Data

(1)

Part II: Mathematical Representations of Social Networks

(100)

Notation for Social Network Data

(23)

Graph Theoretic Notation

(6)

A Single Relation

(2)

xcirc;Multiple Relations

(2)

Summary

(2)

Sociometric Notation

(7)

Single Relation

(2)

Multiple Relations

(2)

Summary

(1)

◯Algebraic Notation

(1)

◯Two Sets of Actors

(4)

&otime;Different Types of Pairs

(1)

◯Sociometric Notation

(2)

Putting It All Together

(3)

Graphs and Matrices

(75)

Why Graphs?

(1)

Graphs

(27)

Subgraphs, Dyads, and Triads

(3)

Nodal Degree

100

(1)

Density of Graphs and Subgraphs

101

(2)

Example: Padgett's Florentine Families

103

(2)

Walks, Trails, and Paths

105

(4)

Connected Graphs and Components

109

(1)

Geodesics, Distance, and Diameter

110

(2)

Connectivity of Graphs

112

(5)

Isomorphic Graphs and Subgraphs

117

(2)

◯Special Kinds of Graphs

119

(2)

Directed Graphs

121

(15)

Subgraphs - Dyads

124

(1)

Nodal Indegree and Outdegree

125

(4)

Density of a Directed Graph

129

(1)

An Example

129

(1)

Directed Walks, Paths, Semipaths

129

(3)

Reachability and Connectivity in Digraphs

132

(2)

Geodesics, Distance and Diameter

134

(1)

◯Special Kinds of Directed Graphs

134

(2)

Summary

136

(1)

Signed Graphs and Signed Directed Graphs

136

(4)

Signed Graph

137

(1)

Signed Directed Graphs

138

(2)

Valued Graphs and Valued Directed Graphs

140

(5)

Nodes and Dyads

142

(1)

Density in a Valued Graph

143

(1)

◯Paths in Valued Graphs

143

(2)

Multigraphs

145

(1)

&otime;Hypergraphs

146

(2)

Relations

148

(2)

Definition

148

(1)

Properties of Relations

149

(1)

Matrices

150

(14)

Matrices for Graphs

150

(2)

Matrices for Digraphs

152

(1)

Matrices for Valued Graphs

153

(1)

Matrices for Two-Mode Networks

154

(1)

ôMatrices for Hypergraphs

154

(1)

Basic Matrix Operations

154

(5)

Computing Simple Network Properties

159

(5)

Summary

164

(1)

Properties

164

(1)

Reflexivity

164

(1)

Symmetry

165

(1)

Transitivity

165

(1)

Summary

165

(2)

Part III: Structural and Locational Properties

167

(178)

Centrality and Prestige

169

(51)

Prominence: Centrality and Prestige

172

(5)

Actor Centrality

173

(1)

Actor Prestige

174

(1)

Group Centralization and Group Prestige

175

(2)

Nondirectional Relations

177

(21)

Degree Centrality

178

(5)

Closeness Centrality

183

(5)

Betweenness Centrality

188

(4)

&otime;Information Centrality

192

(6)

Directional Relations

198

(17)

Centrality

199

(3)

Prestige

202

(8)

A Different Example

210

(5)

Comparisons and Extensions

215

(5)

Structural Balance and Transitivity

220

(29)

Structural Balance

222

(11)

Signed Nondirectional Relations

223

(5)

Signed Directional Relations

228

(2)

◯Checking for Balance

230

(2)

An Index for Balance

232

(1)

Summary

232

(1)

Clusterability

233

(6)

The Clustering Theorems

235

(3)

Summary

238

(1)

Generalizations of Clusterability

239

(4)

Empirical Evidence

239

(1)

◯Ranked Clusterability

240

(2)

Summary

242

(1)

Transitivity

243

(4)

Conclusion

247

(2)

Cohesive Subgroups

249

(42)

Background

250

(3)

Social Group and Subgroup

250

(2)

Notation

252

(1)

Subgroups Based on Complete Mutuality

253

(4)

Definition of a Clique

254

(1)

An Example

254

(2)

Considerations

256

(1)

Reachability and Diameter

257

(6)

n-cliques

258

(1)

An Example

259

(1)

Considerations

260

(1)

n-clans and n-clubs

260

(2)

Summary

262

(1)

Subgroups Based on Nodal Degree

263

(4)

k-plexes

265

(1)

k-cores

266

(1)

Comparing within to Outside Subgroup Ties

267

(3)

LS Sets

268

(1)

Lambda Sets

269

(1)

Measures of Subgroup Cohesion

270

(3)

Directional Relations

273

(4)

Cliques Based on Reciprocated Ties

273

(1)

Connectivity in Directional Relations

274

(1)

n-cliques in Directional Relations

275

(2)

Valued Relations

277

(6)

Cliques, n-cliques, and k-plexes

278

(4)

Other Approaches for Valued Relations

282

(1)

Interpretation of Cohesive Subgroups

283

(1)

Other Approaches

284

(6)

Matrix Permutation Approaches

284

(3)

Multidimensional Scaling

287

(3)

◯Factor Analysis

290

(1)

Summary

290

(1)

Affiliations and Overlapping Subgroups

291

(54)

Affiliation Networks

291

(1)

Background

292

(6)

Theory

292

(2)

Concepts

294

(1)

Applications and Rationale

295

(3)

Representing Affiliation Networks

298

(9)

The Affiliation Network Matrix

298

(1)

Bipartite Graph

299

(4)

Hypergraph

303

(3)

◯Simplices and Simplicial Complexes

306

(1)

Summary

306

(1)

An example: Galaskiewicz's CEOs and Clubs

307

(1)

One-mode Networks

307

(5)

Definition

307

(2)

Examples

309

(3)

Properties of Affiliation Networks

312

(14)

Properties of Actors and Events

312

(2)

Properties of One-mode Networks

314

(8)

Taking Account of Subgroup Size

322

(2)

Interpretation

324

(2)

&otime;Analysis of Actors and Events

326

(16)

&otime;Galois Lattices

326

(8)

&otime;Correspondence Analysis

334

(8)

Summary

342

(3)

Part IV: Roles and Positions

345

(158)

Structural Equivalence

347

(47)

Background

348

(8)

Social Roles and Positions

348

(3)

An Overview of Positional and Role Analysis

351

(3)

A Brief History

354

(2)

Definition of Structural Equivalence

356

(5)

Definition

356

(1)

An Example

357

(2)

Some Issues in Defining Structural Equivalence

359

(2)

Positional Analysis

361

(5)

Simplification of Multirelational Networks

361

(2)

Tasks in a Positional Analysis

363

(3)

Measuring Structural Equivalence

366

(9)

Euclidean Distance as a Measure of Structural Equivalence

367

(1)

Correlation as a Measure of Structural Equivalence

368

(2)

Some Considerations in Measuring Structural Equivalence

370

(5)

Representation of Network Positions

375

(16)

Partitioning Actors

375

(10)

Spatial Representations of Actor Equivalences

385

(3)

Ties Between and Within Positions

388

(3)

Summary

391

(3)

Blockmodels

394

(31)

Definition

395

(2)

Building Blocks

397

(11)

Perfect Fit (Fat Fit)

398

(1)

Zeroblock (Lean Fit) Criterion

399

(1)

Oneblock Criterion

400

(1)

α Density Criterion

400

(1)

Comparison of Criteria

401

(1)

Examples

401

(5)

Valued Relations

406

(2)

Interpretation

408

(15)

Actor Attributes

408

(3)

Describing Individual Positions

411

(6)

Image Matrices

417

(6)

Summary

423

(2)

Relational Algebras

425

(36)

Background

426

(2)

Notation and Algebraic Operations

428

(5)

Composition and Compound Relations

429

(3)

Properties of Composition and Compound Relations

432

(1)

Multiplication Tables for Relations

433

(9)

Multiplication Tables and Relational Structures

435

(4)

An Example

439

(3)

Simplification of Role Tables

442

(7)

Simplification by Comparing Images

443

(2)

&otime;Homomorphic Reduction

445

(4)

&otime;Comparing Role Structures

449

(11)

Joint Homomorphic Reduction

451

(1)

The Common Structure Semigroup

452

(1)

An Example

453

(4)

Measuring the Similarity of Role Structures

457

(3)

Summary

460

(1)

Network Positions and Roles

461

(42)

Background

462

(6)

Theoretical Definitions of Roles and Positions

462

(2)

Levels of Role Analysis in Social Networks

464

(2)

Equivalences in Networks

466

(2)

Structural Equivalence, Revisited

468

(1)

Automorphic and Isomorphic Equivalence

469

(4)

Definition

470

(1)

Example

471

(1)

Measuring Automorphic Equivalence

472

(1)

Regular Equivalence

473

(10)

Definition of Regular Equivalence

474

(1)

Regular Equivalence for Nondirectional Relations

475

(1)

Regular Equivalence Blockmodels

476

(3)

◯A Measure of Regular Equivalence

479

(2)

An Example

481

(2)

``Types'' of Ties

483

(4)

An Example

485

(2)

Local Role Equivalence

487

(7)

Measuring Local Role Dissimilarity

488

(3)

Examples

491

(3)

&otime;Ego Algebras

494

(8)

Definition of Ego Algebras

496

(1)

Equivalence of Ego Algebras

497

(1)

Measuring Ego Algebra Similarity

497

(2)

Examples

499

(3)

Discussion

502

(1)

Part V: Dyadic and Triadic Methods

503

(100)

Dyads

505

(51)

An Overview

506

(2)

An Example and Some Definitions

508

(2)

Dyads

510

(12)

The Dyad Census

512

(1)

The Example and Its Dyad Census

513

(1)

An Index for Mutuality

514

(4)

&otime;A Second Index for Mutuality

518

(2)

◯Subgraph Analysis, in General

520

(2)

Simple Distributions

522

(6)

The Uniform Distribution - A Review

524

(2)

Simple Distributions on Digraphs

526

(2)

Statistical Analysis of the Number of Arcs

528

(7)

Testing

529

(4)

Estimation

533

(2)

&otime;Conditional Uniform Distributions

535

(4)

Uniform Distribution, Conditional on the Number of Arcs

536

(1)

Uniform Distribution, Conditional on the Outdegrees

537

(2)

Statistical Analysis of the Number of Mutuals

539

(5)

Estimation

540

(2)

Testing

542

(1)

Examples

543

(1)

&otime;Other Conditional Uniform Distributions

544

(8)

Uniform Distribution, Conditional on the Indegrees

545

(2)

The U\MAN Distribution

547

(3)

More Complex Distributions

550

(2)

Other Research

552

(3)

Conclusion

555

(1)

Triads

556

(47)

Random Models and Substantive Hypotheses

558

(1)

Triads

559

(16)

The Triad Census

564

(10)

The Example and Its Triad Census

574

(1)

Distribution of a Triad Census

575

(10)

&otime;Mean and Variance of a k-subgraph Census

576

(3)

Mean and Variance of a Triad Census

579

(2)

Return to the Example

581

(1)

Mean and Variance of Linear Combinations of a Triad Census

582

(2)

A Brief Review

584

(1)

Testing Structural Hypotheses

585

(13)

Configurations

585

(5)

From Configurations to Weighting Vectors

590

(2)

From Weighting Vectors to Test Statistics

592

(3)

An Example

595

(1)

Another Example --- Testing for Transitivity

596

(2)

Generalizations and Conclusions

598

(3)

Summary

601

(2)

Part VI: Statistical Dyadic Interaction Models

603

(122)

Statistical Analysis of Single Relational Networks

605

(70)

Single Directional Relations

607

(28)

The Y-array

608

(4)

Modeling the Y-array

612

(7)

Parameters

619

(14)

&otime;Is p1 a Random Directed Graph Distribution?

633

(1)

Summary

634

(1)

Attribute Variables

635

(14)

Introduction

636

(1)

The W-array

637

(3)

The Basic Model with Attribute Variables

640

(6)

Examples: Using Attribute Variables

646

(3)

Related Models for Further Aggregated Data

649

(7)

Strict Relational Analysis --- The V-array

651

(3)

Ordinal Relational Data

654

(2)

◯Nondirectional Relations

656

(2)

A Model

656

(1)

An Example

657

(1)

&otime;Recent Generalizations of p1

658

(4)

&otime;Single Relations and Two Sets of Actors

662

(3)

Introduction

662

(1)

The Basic Model

663

(1)

Aggregating Dyads for Two-mode Networks

664

(1)

Computing for Log-linear Models

665

(8)

Computing Packages

666

(5)

From Printouts to Parameters

671

(2)

Summary

673

(2)

Stochastic Blockmodels and Goodness-of-Fit Indices

675

(50)

Evaluating Blockmodels

678

(14)

Goodness-of-Fit Statistics for Blockmodels

679

(9)

Structurally Based Blockmodels and Permutation Tests

688

(1)

An Example

689

(3)

Stochastic Blockmodels

692

(27)

Definition of a Stochastic Blockmodel

694

(2)

Definition of Stochastic Equivalence

696

(1)

Application to Special Probability Functions

697

(6)

Goodness-of-Fit Indices for Stochastic Blockmodels

703

(3)

◯Stochastic a posteriori Blockmodels

706

(2)

Measures of Stochastic Equivalence

708

(1)

Stochastic Blockmodel Representations

709

(3)

The Example Continued

712

(7)

Summary: Generalizations and Extensions

719

(6)

Statistical Analysis of Multiple Relational Networks

719

(2)

Statistical Analysis of Longitudinal Relations

721

(4)

Part VII: Epilogue

725

(10)

Future Directions

727

(8)

Statistical Models

727

(2)

Generalizing to New Kinds of Data

729

(2)

Multiple Relations

730

(1)

Dynamic and Longitudinal Network Models

730

(1)

Ego-centered Networks

731

(1)

Data Collection

731

(1)

Sampling

732

(1)

General Propositions about Structure

732

(1)

Computer Technology

733

(1)

Networks and Standard Social and Behavioral Science

733

(2)

Appendix A Computer Programs

735

(3)

Appendix B Data

738

(18)

References

756

(46)

Name Index

802

(9)

Subject Index

811

(8)

List of Notation

819

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Social Network Analysis: Methods and Applications

Summary

Table of Contents

Supplemental Materials