Social Network Analysis with Applications

Written by military, industry, and business professionals, this book introduces readers to social network analysis, the new and emerging topic that has recently become of significant use for industry, management, law enforcement, and military practitioners for identifying both vulnerabilities and opportunities in collaborative networked organizations.

Focusing on models and methods for the analysis of organizational risk, Social Network Analysis with Applications provides easily accessible, yet comprehensive coverage of network basics, centrality measures, social link theory, subgroup analysis, relational algebra, data sources, and more. Examples of mathematical calculations and formulas for social network measures are also included.

Along with practice problems and exercises, this easily accessible book covers:

• The basic concepts of networks, nodes, links, adjacency matrices, and graphs
• Mathematical calculations and exercises for centrality, the basic measures of degree, betweenness, closeness, and eigenvector centralities
• Graph-level measures, with a special focus on both the visual and numerical analysis of networks
• Matrix algebra, outlining basic concepts such as matrix addition, subtraction, multiplication, and transpose and inverse calculations in linear algebra that are useful for developing networks from relational data
• Meta-networks and relational algebra, social links, diffusion through networks, subgroup analysis, and more

An excellent resource for practitioners in industry, management, law enforcement, and military intelligence who wish to learn and apply social network analysis to their respective fields, Social Network Analysis with Applications is also an ideal text for upper-level undergraduate and graduate level courses and workshops on 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/Adaptive 220

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

Secondary: Final year undergraduates and entry–level graduate students.

IAN McCULLOH, PhD, holds academic appointments at several institutions to include Curtin University Business School. He consults industry to increase collaboration in knowledge-intensive organizations and educates military intelligence professionals to more ethically and effectively target enemy networks. He has supported the U.S. Military with network analysis to include service in Afghanistan and Iraq.

HELEN ARMSTRONG, PhD, is an Associate Professor in the School of Information Systems at Curtin University in Perth, Australia. She has more than twenty years' experience teaching and conducting research in ICT network security, analyses of networks and systems, information systems strategy, and management and problem solving in business environments. She works closely with industry in the application of network analyses for business problem solving and risk analyses.

ANTHONY JOHNSON, PhD, is an Associate Professor in the Department of Mathematical Sciences at the United States Military Academy at West Point. He has served in a variety of positions ranging from Fiber Optic Cable Network Engineer for the White House Communications Agency to the Chief of Counter Improvised Explosive Device (CIED) Operations in Iraq where he applied linear algebra and graph theory to exploit terrorist networks.