Short answers, pulled from the story.
A social network is a social structure consisting of a set of social actors, such as individuals or organizations, connected by dyadic ties and other social interactions. The social network perspective analyzes these structures to identify local and global patterns, locate influential entities, and examine how networks change over time.
Jacob L. Moreno is credited with developing the first sociograms in the 1930s. He created them to study interpersonal relationships by systematically recording and analyzing social interaction in small groups, especially classrooms and work groups.
The strength of weak ties is a theory developed by Mark Granovetter, who found that loose connections to acquaintances can be more valuable for finding new information and innovation than close friendships. Members of tight cliques tend to share the same knowledge, so non-redundant information usually arrives through weaker, more distant ties.
A structural hole is the gap between two clusters of people who hold different, non-overlapping information and would not otherwise be in contact. A person whose network bridges structural holes acts as a broker, gaining access to diverse information and opportunities. Ronald Burt's 2004 study of 673 managers found that those who bridged such holes were better paid, better evaluated, and more likely to be promoted.
Social network analysis operates at micro, meso, and macro levels. The micro level focuses on individuals, dyads, triads, and small subgroups. The meso level examines organizations and mid-size populations, including exponential random graph models and scale-free networks. The macro level traces aggregate outcomes across large populations, such as economic resource transfers or the diffusion of innovations.
Social network analysis is used in epidemiology, models of patient communication, disease prevention, mental health diagnosis, and the study of health care organizations. Respondent-driven sampling, a network-based technique in which survey respondents recommend further respondents, allows researchers to estimate and reach populations that are otherwise hard to count, including homeless people and intravenous drug users.