Network Density

Social Network Analysis

Social network analysis is a quantitative method widely used to investigate a social environment with a focus on the relationship among social entities and the pattern derived from the relationships. Researchers’ interest in modeling the property of pairwise relation in a network can be traced back to Leonhard Euler’s work, Seven Bridges of Königsberg, in 1736, which laid the foundation for the graph theory in mathematics. In the 1930s, Gestalt psychologist Jacob Moreno developed sociograms to visualize the social structure of a group of elementary school students. Motivated by the use of sociograms, in the 1940s and 1950s, plenty of analytic techniques and mathematical models were developed to measure network properties, such as reciprocity, mutuality, balance, and transitivity. At the same time, network analysis was intensively used by anthropologists and social psychologists in studying complex society and human communication. During the 1980s, the application of log linear models and Paul Holland [Page 1144]and Samuel Leinhardt’s p1 model in network analysis expedited the use of the method. Ever since, social network analysis was extended to modeling nominal, ordinal data, as well as multivariate relational and longitudinal data.

The Calculation of Network Density

In social network analysis, the index of network density is simply defined as the ratio of observed edges to the number of possible edges for a given network. Before calculating network density, it is necessary to differentiate between two types of networks: undirected networks and directed networks. In undirected networks, ties are nondirectional. That is, for each dyadic relation, there is no way to distinguish between the “initiator” and “receiver.” In a therapeutic group, the working alliance between the therapist and each individual client is an example of a nondirectional relationship, and the whole therapeutic group can be seen as an undirected network. By contrast, in a directed network, each tie has a direction, orienting from “initiator” to “receiver.” For example, a sociogram based on the aggression of a group of high school students is a directed network.

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