Social networks analysis

Summary:Social networks can be described and analyzed using graph theory.

A social network is a set of actors and the relationships that connect them. The actors are usually people, but may be other individual or collective actors, such as organizations, gangs, clubs, municipalities, nations, or social animals. Social network analysis is a cross-disciplinary method for analyzing social networks that integrates techniques from science, social science, mathematics, computer science, communication, and business. In keeping with its diverse origins, various types of social relationships have been studied using social network analysis, such as friendship, sexual relationships, kinship and genealogy, competitions, collaboration, and disease spread.

Sociogram, Sociomatrix, Graph, and Network

Modern social network analysis can be traced to Austro-American psychiatrist Jacob Levy Moreno, though many of the methods he employed in his work had been used before in a more piecemeal fashion. For example, French probabilist Irénée-Jules Bienaymé modeled the disappearance of closed families (for example, aristocrats) and family names in the nineteenth century. In his 1934 book Who Shall Survive, Moreno used diagrams he called “sociograms” to analyze friendships among girls in a training school in New York State. The girls were represented by points, and pairs of girls who were friends were connected by a line. In sociograms of relationships such as liking, which are not necessarily reciprocated, an arrowhead indicates the direction.

While very simple social networks can be analyzed by visual inspection, the power of social network analysis arises from the conceptualization of the sociogram as a mathematical graph, which can be analyzed using the concepts and methods of graph theory. Moreover, a graph can be represented by a square adjacency matrix in which each row and column represent a point, and the cell entries represent the presence or absence of lines between points. A graph can be generalized in several ways. Lines can have numerical values representing, for example, the strength, intensity, or frequency of a relationship. There can be multiple types of lines between pairs of actors, each representing one type of relationship. Actors can have various attributes with numerical values or qualitative labels. In social network analysis, real-life social networks are modeled by mathematical networks, then the properties of the networks are analyzed mathematically in order to draw conclusions about the structure of the social relationships.

Social Cohesion

Social cohesion is a fundamental issue in the social sciences; it is the “glue” or bond that holds a social group together. According to social network analysis, it is the network of social ties among members of the group. Therefore, to measure the level of social cohesion in a social group or subgroup, one must measure the extent of ties among the members. The density of ties among members is the simplest measure of connectedness. It is defined as the ratio of the number of actual ties to the number of possible ties and ranges from 0 to 1. In a network with one symmetric (undirected) type of tie, and k members, the total possible number of ties is

A network in which every actor is connected is called a “complete” graph, or a “clique.”

It is easy to imagine four people all being friends with one another but less realistic to postulate a clique with a large number of members. For example, in a clique with 30 members, each would have to maintain ties with the 29 other members—an onerous task. Limits on human beings’ time, energy, and memory constrain the number of people with whom they can maintain social ties. Therefore, social networks tend to become more sparse (the ties become less dense) as they become larger. Residents of a small village may know all the other residents, but this is impossible for city-dwellers. Thus, the village will tend to be more socially cohesive than the city. Density of ties has also been used to study social cohesion in such areas of social life as marriage, the family, small groups in laboratories, community elites, intercorporate relationships such as share ownership and interlocking directorates, scientific communities, and the spread of ideas and diseases.

The overall density of ties is a rather crude measure of connectivity and cohesion in a social network, because it is insensitive to local variations. Real-life social networks tend to contain islands of actors tied relatively densely to one another but disconnected or only loosely connected by sparse ties to other such islands. In the friendship network of a high school, there are likely to be a number of small cliques, perhaps loosely connected into larger subgroups that are in turn perhaps totally disconnected from one another. Detection of relatively cohesive subgroups in a network and delineation of their articulation into larger, less cohesive groups are a major theme in social network analysis.

Centrality

The centrality of an actor in a network is an important attribute, because centrality is associated with power, prestige, prominence, and popularity. In a network of ties representing flows or potential flows of valued social goods, such as information, a central actor is in a privileged position for both reception and transmission. The centrality of an actor may be intuitively evident from visual inspection of the drawing of a graph, especially if the graph is small or highly centralized. In larger graphs, a precise definition and formula are needed. The four main definitions of centrality are degree, closeness, betweenness, and power (or “eigenvector”) centrality.

Degree centrality is the proportion of the other actors to which an actor is directly connected. The closeness centrality of an actor is based on how close the actor is to each of the other actors in the network and is the inverse of distance. The betweenness centrality of an actor is the extent to which the actor is “between” other actors; in other words, how often the shortest paths between pairs of other actors pass through the actor. Power centrality is defined recursively taking into account the power centrality of the actors to which an actor is adjacent.

Applications of Social Networks

The popular party game Six Degrees of Kevin Bacon tries to connect any movie actor to actor Kevin Bacon via costars in movies using the shortest number of steps. That value is an actor’s Bacon Number. The Web site “The Oracle of Bacon,” originally implemented in 1996, can be used to find the shortest path for any actor that can be linked to Kevin Bacon. The average path length as of September, 2010, was about three. It also allows a user to find a measure of centrality for the Hollywood network based around any actor in the database in terms of the average path length.

On a more personal level, the social network Web site Facebook includes an application called Friend Wheel that lets users visualize the interconnections among their friends as nodes and ties. Further, it selectively arranges the friends’ names around the circumference of the wheel so that closely-knit groups or cliques are placed together and color-coded. Thomas Fletcher, a computer science and mathematics student at Bath University, developed the application and made it available in 2007.

Harkening back to Moreno’s study, in 1995 a team of sociologists was the first to map the romantic and sexual relationships of an entire high school. Unlike similar adult networks, which tend to have several highly interconnected cores with loose interconnections (like airline hubs), the students were connected via long chains, more like a rural phone network. One chain linked 288 of the 573 romantically active students, though there were also many unconnected dyads or triads. Researchers attributed this finding in part to the often-elaborate teenage social rules about who may date. The surprising finding had important implications for educational practices like sex education programs.

Bibliography

Bearman, P. S., J. Moody, and K. Stovel. “Chains of Affection: The Structure of Adolescent Romantic and Sexual Networks.” American Journal of Sociology 110, no. 1 (2004).

Furht, Borko. Handbook of Social Network Technologies and Applications. New York: Springer, 2010.

Moreno, Jacob L. Who Shall Survive? Washington, DC: Nervous and Mental Disease Publishing, 1934.

Wasserman, Stanley, and Katherine Faust. Social Network Analysis. New York: Cambridge University Press, 1994.