The term “network” denotes a central concept in the social sciences. The underlying idea of a structure that consists of elements (sometimes also called points, nodes, or vertices) and their relations (called lines, edges, arcs, or connections) has been used to illustrate and explain such diverse things as human action, information exchange in communication processes, peer groups, social formations, organizational coordination, markets and even whole societies, to name but a few of the application contexts. In many of these cases, the term “network” is used in a purely metaphorical sense, which remotely refers to a web-like phenomenon. However, it can also stand for a clearly defined analytical concept, which can be described on the basis of a formal mathematical language. By applying mathematical network logics to the analysis of social phenomena, researchers gain insight into their structures, i.e., the arrangement of the constituent elements and their connections. Furthermore, social phenomena can be compared on the basis of their (structural) network properties when using a standardized mathematical description language and uniform measurements.

## Roots And Development Of The Network Idea

As with many approaches in social sciences, there is not just one historical source of network analysis. Some of the mathematical and logical foundations were laid in the eighteenth century with so-called graph theory. As early as 1737, Leonhard Euler introduced some basic ideas in a mathematical proof, including the concept of the “graph” – a figure consisting of points and lines, whose structural properties can be transformed into mathematical formulas. Since then, these fundamental assumptions have been further developed, resulting in a unique mathematical and logical perspective, offering descriptions and explanations of complex phenomena, in both the natural and the social sciences.

The more specific roots of network analysis in social analysis are diverse, to say the least, and various opinions on the lineage of network analysis exist. In social anthropology and social psychology, network approaches have been discussed by several schools of thought, starting in the first half of the twentieth century. To the public, probably one of the best-known psychological approaches in this field is Jacob Moreno’s sociometry, with origins in the 1930s. Moreno introduced the sociogram, a way of visually depicting the structure of social groups in the form of points (the persons) and directed lines (the social relationships). There were also other psychologists at that time, like Kurt Lewin and Fritz Heider, who were working on the interrelations of social structures and the behavior of individuals or groups.

In contrast to psychologists, who mostly focused on smaller groups of people, social anthropologists were interested in the structure of larger social entities. Alfred Reginald Radcliffe-Brown in the 1930s was one of the first actually to use the term “network” – still in a metaphorical way – to describe social structures . In the following decades, Radcliffe-Brown’s basic network approach was developed both in the US by scholars like Lloyd Warner, Elton Mayo, and George C. Homans, and in the UK by John A. Barnes, J. Clyde Mitchell, and others. Barnes’s studies on kinship and community structures in the 1950s, in particular, can be seen as an important step in expanding the approach toward a modern network analysis, since he understood networks as a structural and logical concept rather than a metaphor. In some later works of his Manchester colleague Mitchell, the social scientific tradition finally met the mathematical approach again: Mitchell applied and developed ideas of graph theory in his sociological studies. In the years since then, network analysis has embraced mathematical models, for example in Harrison C. White’s works on block modeling in the 1970s; recently, the rapid development of computer technology has offered further possibilities, especially in the analysis of large networks.

In communication studies, network analysis still plays a minor role, especially when compared to the number of studies based on traditional data analysis. For example, Schenk has analyzed the importance of interpersonal networks for opinion building and the relationship of social networks and mass media, starting in the 1980s. However, it was not until lately that the network idea became more popular in communication studies – a development maybe somewhat related to the growing importance of computer networks in the discussion of media and communication processes.

## Network Definition And Concepts Of Analysis

As described above, the term “network” has a clearly defined meaning in social network analysis:

- A network is a specific structure, consisting of a number of points and their connecting lines.
- In most cases, the points refer to individuals, sometimes also groups or companies, and the lines depict their relations (based on the analysis of friendship or hate, power and influence, economic partnerships, to name but a few of the relationships that have been used in network analysis). That said, social network analysis is not necessarily restricted to actor or group networks – the researcher is certainly free in the choice of elements, and some have already proven that network analysis can be applied to other types of networks as well (like action networks, which focus on human action instead of the relations between human beings or social entities).
- The network structure can be described using formal mathematical language and depicted using network graphs (Figure 1).

Certainly, networks can be further qualified beyond this very rough outline. For example, one can differentiate between a directed and an undirected network. While the latter just focuses on the existence of relations, thus depicting them in the network graph via lines, the directed version includes information on the direction of relations, for example if point A influences point B (usually depicted with an arrow instead of a simple line). Relations and influences cannot only be identified by the connections of the elements and the direction of these lines, though – they can also be described by their intensity. If information about the relation’s intensity is included in the network graph (for example, by adding a number indicating the strength of a line), one speaks of valued graphs, in contrast to binary graphs, which only hold information about whether a line exists or not. Last but not least, there are not only networks that combine elements of one type. Sometimes, researchers are interested in the links between different elements (for example, individuals and certain events). The resulting “mixed” networks, which combine two distinct groups of elements, are called “bipartite.”

Figure 1 A network graph and its corresponding adjacency matrix

In many publications, network researchers use depictions of networks in the forms of graphs. This information can also be contained in data matrices equivalent to the graphs. For data (re)organization and analysis, these matrices are much more important than the actual graphics, which are limited by the possibilities of two-dimensional visualization. In contrast to standard statistical datasets, network matrices contain information on the relations of elements, rather than various variable values in columns and cases in rows (or vice versa). The most important type of organizing relational data is the so-called adjacency matrix (see Fig. 1). Here, all points of the network are organized in both rows and columns. In the individual cells, one can find a number that represents the relation between the row and column elements, which can be binary (existing/not existing) or valued. Another type of matrix is the affiliation matrix, which shows the relations between elements of different types (like actors and events, as described above).

On the basis of data matrices, the researcher can calculate various indices focusing on specific network properties. There are mathematical descriptions for the characteristics of individual elements, network structures, and the attributes of a whole network. Using these, the researcher can answer questions like: How important or central is an element in the network? Are there areas of high density in a network, hinting at strongly connected social groups? How big, dense, and centralized is a given network in comparison to another network? While the mathematical analysis of network data offers interesting solutions, there are still some areas in network analysis that need to be developed further. For example, there are no common measures for dynamic networks – most network analysts merely focus on static networks, which are very often just snapshots of a social situation. While there are solutions (for example, measures of network stability), they are not widely accepted so far. So network analysis is still seeing many changes and innovation, unlike other, more conventional, approaches to social reality.

## Applications Of Network Analysis In Communication Studies

While network analysis has been successfully applied in the larger field of social sciences, there have not yet been many reports in communication studies that use this approach, at least when compared with other methods of analysis. As described above, there has been some empirical work on interpersonal networks. These researchers chose to follow the classic approach of network analysis, which defines humans as elements of the networks and focuses on the relations of these actors. In a similar vein, there are also several studies on the structure of media markets that apply a network logic, in this case with the basic elements of corporate actors (media companies). When going below the level of individual actors or groups as elements, one could use the network logic as well, for example when trying to find relations between human actions or communicative acts. However, the approach is not restricted to groups, individuals, or their actions; it can also be useful whenever there is relational data, as described above. For example, textual information could be analyzed in this way as well, looking for links between information elements. It will be interesting to see how network analysis develops in the future, both in theory and in empirical practice.

**References:**

- Barnes, J. A. (1972). Social networks. Reading, MA: Addison-Wesley, pp. 1–29.
- Mitchell, J. C. (1969). The concept and use of social networks. In J. C. Mitchell (ed.), Social networks in urban situations. Manchester: Manchester University Press, pp. 1–50.
- Schenk, M. (1995). Soziale Netzwerke und Massenmedien: Untersuchungen zum Einfluß der persönlichen Kommunikation [Social networks and mass media: Studies on the influence of personal communication]. Tübingen: Mohr.
- Scott, J. (2000). Social network analysis: A handbook. London: Sage.
- Scott, J. (ed.) (2002). Social networks: Critical concepts in sociology. London: Routledge.
- Wasserman, S., & Faust, K. (1994). Social network analysis: Methods and applications. Cambridge: Cambridge University Press.
- White, H. C. (1963). An anatomy of kinship: Mathematical models for structures of cumulated roles. Englewood Cliffs, NJ: Prentice Hall.