Graphing Social Networks

Graphing Social Networks - June 23, 2001 Graphical...

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Graphical Techniques for Exploring Social Network Data Linton C. Freeman University of California, Irvine Social network analysts study the structural patterning of the ties that link social actors. For the most part, they seek to uncover two kinds of patterns: (1) those that reveal subsets of actors that are organized into cohesive social groups, and (2) those that reveal subsets of actors that occupy equivalent social positions, or roles. To uncover patterns of those kinds, network analysts collect and examine data on actor-to-actor ties. Such data record who is connected to whom and/or how closely they are connected. Typically, the data are organized into square, N -dimensional, N -by- N matrices where the N rows and the N columns both refer to the social actors being studied. Cell entries in these matrices indicate either the presence/absence or the strength of some social relationship linking the row actor to the column actor. In the present discussion, we will deal only with symmetric relationships where, given a connection from actor i to actor j , actor j is also connected to i in the same way. Network analysts sometimes use standard statistical procedures in examining their actor-by-actor matrices. And there are several statistical modeling tools that have been developed specifically for network data (Holland and Leinhardt, 1981; Wasserman and Pattison, 1996). But these tools were designed primarily for testing hypotheses. They do not provide a simple direct way to explore the patterning of network data—one that will permit an investigator to “see” groups and positions. The aim of the present paper is to introduce and illustrate such an exploratory device. In the next section, I will show some ways to create visual images that can be used to display the kinds of structure of interest to
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2 network analysts. Then, following that, I will show how those images can be adapted to help to uncover both the antecedents and the consequences of observed network structure. Visual Images Jacob Moreno (1932, 1934) was the first to use visual images to display the patterning of linkages among social actors. In Moreno’ s images, each actor was represented by a point, and each link was shown by a line connecting a pair of points. One of his earliest images (Moreno 1932, p. 101) is reproduced as Figure 1. He characterized that image as showing “a group in which two dominating individuals are strongly united both directly and indirectly through other individuals.” Thus, Moreno viewed that picture as a display of both cohesiveness (“strongly united”) and social roles (“dominating individuals”). Figure 1. Moreno’s Early Image
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3 In this early work Moreno demonstrated “that variations in the locations of points could be used to stress important structural patterns in the data” (Freeman, 2000). Figure 2, for example, shows his image of friendship choices among fourth graders (Moreno 1934, p. 38). There he used triangles to designate boys, and circles to designate girls. He also used
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Graphing Social Networks - June 23, 2001 Graphical...

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