Social Network Analysis with Applications

A comprehensive introduction to social network analysis thathones in on basic centrality measures, social links, subgroupanalysis, data sources, and more

Written by military, industry, and business professionals, thisbook introduces readers to social network analysis, the new andemerging topic that has recently become of significant use forindustry, management, law enforcement, and military practitionersfor identifying both vulnerabilities and opportunities incollaborative networked organizations.

Focusing on models and methods for the analysis oforganizational risk, Social Network Analysis withApplications provides easily accessible, yet comprehensivecoverage of network basics, centrality measures, social linktheory, subgroup analysis, relational algebra, data sources, andmore. Examples of mathematical calculations and formulas for socialnetwork measures are also included.

Along with practice problems and exercises, this easilyaccessible book covers:

The basic concepts of networks, nodes, links, adjacencymatrices, and graphs Mathematical calculations and exercises for centrality, thebasic measures of degree, betweenness, closeness, and eigenvectorcentralities Graph–level measures, with a special focus on both the visualand numerical analysis of networks Matrix algebra, outlining basic concepts such as matrixaddition, subtraction, multiplication, and transpose and inversecalculations in linear algebra that are useful for developingnetworks from relational data Meta–networks and relational algebra, social links, diffusionthrough networks, subgroup analysis, and more

An excellent resource for practitioners in industry, management,law enforcement, and military intelligence who wish to learn andapply social network analysis to their respective fields, SocialNetwork Analysis with Applications is also an ideal text forupper–level undergraduate and graduate level courses and workshopson the subject.

List of Figures xi

List of Tables xv

Foreword xvii

Preface xix

Acknowledgments xxi

Introduction xxv

Part I Network Basics

Chapter 1 What is a Network? 3

1.1 Basic Network Concepts 4

1.2 Adjacency Matrices, Graphs, and Notation 4

1.3 Nodes and Links 6

1.4 Good Will Hunting Problem 9

1.5 Formal and Informal Networks 13

1.6 Summary 18

Chapter 2 Centrality Measures 29

2.1 What is Centrality and Why do we Study It?29

2.2 Calculating Nodal Centrality Measures 33

2.3 Directed Networks and Centrality Measures 46

2.4 Location in the Network 46

2.5 Summary 52

Chapter 3 Graph Level Measures 69

3.1 Density 70

3.2 Diameter 71

3.3 Centralization 73

3.4 Average Centralities 77

3.5 Network Topology 78

3.6 Summary 86

Part II Social Theory

Chapter 4 Social Links 109

4.1 Individual Actors 110

4.2 Social Exchange Theory 111

4.3 Social Forces 113

4.4 Graph Structure 120

4.5 Agent Optimization Strategies in Networks 121

4.6 Hierarchy of Social Link Motivation 124

4.7 Summary

Chapter 5 Subgroup Analysis 129

5.1 Subgroups 129

5.2 Organizational Theory 130

5.3 Random Groups 133

5.4 Heuristics for Subgroup Identification 133

5.5 Analysis Methods 135

5.6 Summary 143

Chapter 6 Diffusion and Influence 149

6.1 Applications for Social Diffusion 149

6.2 Strain Theory 151

6.3 Social Context 152

6.4 Group Impacts on Diffusion 156

6.5 Network Structure and Diffusion 158

6.6 Group Influence Strategies and Bases of Power 160

6.7 Summary 165

Part III Data

Chapter 7 Meta–Networks and Relational Algebra 173

7.1 Modes of Data 174

7.2 Source, Target, Direction 174

7.3 Mulitmode Networks 176

7.4 Bridging a Meta–Network 180

7.5 Strength of Ties 182

7.6 Summary 183

Chapter 8 Sources of Data 189

8.1 Network Sampling 189

8.2 Measuring Links 191

8.3 Data Quality 195

8.4 Additional Ethnographic Data Collection Methods 196

8.5 Anonymity Issues 198

8.6 Summary 199

Part IV Organizational Risk

Chapter 9 Organizational Risk 205

9.1 What is risk? 205

9.2 Measures of Centrality and Risk 207

9.3 Other Risk Measures 216

9.4 The Right Network: Efficient Versus Learning/Adaptive220

9.5 Network Threats and Vulnerabilities 223

9.6 Thickening a Network 226

9.7 Thinning a Network 227

9.8 Process of Organizational Risk Analysis 228

9.9 Summary of Main Points 231

Appendix A: Matrix Algebra Primer 235

Appendix B: Tables of Data and Networks 241

Appendix C: Five Points of a Graph 273

Index 281

IAN McCULLOH, PhD, holds academic appointments at severalinstitutions to include Curtin University Business School. Heconsults industry to increase collaboration in knowledge–intensiveorganizations and educates military intelligence professionals tomore ethically and effectively target enemy networks. He hassupported the U.S. Military with network analysis to includeservice in Afghanistan and Iraq.

HELEN ARMSTRONG, PhD, is an Associate Professor in theSchool of Information Systems at Curtin University in Perth,Australia. She has more than twenty years′ experience teaching andconducting research in ICT network security, analyses of networksand systems, information systems strategy, and management andproblem solving in business environments. She works closely withindustry in the application of network analyses for businessproblem solving and risk analyses.

ANTHONY JOHNSON, PhD, is an Associate Professor in theDepartment of Mathematical Sciences at the United States MilitaryAcademy at West Point. He has served in a variety of positionsranging from Fiber Optic Cable Network Engineer for the White HouseCommunications Agency to the Chief of Counter Improvised ExplosiveDevice (CIED) Operations in Iraq where he applied linear algebraand graph theory to exploit terrorist networks.