The inclusion of mathematical calculations is central to our approach in this text. Many in the field prefer to present social network analysis by hiding the mathematics and relying on computer software to identify centrality. We contend that this is a critical mistake in the pedagogy of network analysis. The authors have taught over 30 courses in social network analysis to over 500 students with varied approaches and consulted with many more colleagues. Those who have learned how to calculate centrality measures by hand calculation, for example, are 11 times more likely to retain an understanding of what the measures mean 1–3 months after the course. Thus, it is not our contention that an individual would use hand calculations on any real-world example. However, in learning to calculate measures by hand, the mathematics leads to an understanding of the underlying principles of social network analysis.
Many practitioners in industry, management, military intelligence, and law enforcement have expressed a growing interest in social network analysis, specif- ically focused on identifying organizational risk. We operationally define organi- zational risk as vulnerability in the social network. This could be a node high in informal power or a rare broker of resources. This could be a point of influence for the diffusion of ideology. There may exist many networks within an organization, such as a friendship network, a resource network, or a knowledge network. One or more of these networks may present organizational risk, while the others do not. In a military or law enforcement application, organizational risk identifies targets for further development and investigation. In an industry or management application, organizational risk identifies informal power brokers that should be included in management decisions, and potential vulnerability from lack of redundancy. The authors attempt to present examples of both.