Visualizing Social Network Data

The two principle methods to visualize social network data are in graphs and matrices. A graph is “a model for a social network with an undirected dichotomous relation; that is, a tie is either present or absent between each pair of actors.”²³⁷ Simply speaking, a graph “consists of points (or nodes) to represent actors and lines (or edges) to represent ties or relations.”²³⁸ The term coined by sociologists to describe these graphs is a sociogram, which will be

234 Ibid., 28.

235 Ibid., 19.

236 Robert A. Hanneman and Mark Riddle, Introduction to Social Methods, (Riverside, CA:

University of California, 2005), under "Chapter 11: Cliques and Subgroups,"

http://www.faculty.ucr.edu/~hanneman/nettext/ (accessed December 7, 2007).

237 Stanley Wasserman and Katherine Faust, Social Network Analysis: Methods and Applications, 94.

238 Robert A. Hanneman and Mark Riddle, Introduction to Social Methods, (Riverside, CA:

University of California, 2005), under "Chapter 5: Using Matrices to Represent Social Relations."

used to describe the graphic representation of proliferation networks. Matrices, in contrast, used to collect data on the relations between actors depicted in a structure of rows and columns. Matrices and the data structure for proliferation events will be described in more detail throughout this chapter. Listed below are a few final concepts that will be used to describe these networks and the relational ties that exist between actors.

a. Levels of Measuring Relations

The ties between actors depicted on a graph can either be binary, signed, or valued. At the most basic level, binary relations describe only whether a tie exists or not.²³⁹ A binary relation can be depicted on a matrix by entering a one at the intersection of column and row between actors that have an identified relationship and with a zero for actors who do not. Representing preferences between actors that have a relationship, such as like or dislike, can be accomplished with signed data. Signed data can be displayed on a graph by assigning “a + to indicate ‘liking,’ zero to indicate ‘don’t care’ and – to indicate a negative choice.”²⁴⁰ Finally, a valued relation between actors can be measured by rank ordering a constant variable that exists such as who each actor likes the

“most, next most, and least.”²⁴¹ The approach taken to represent relationships between actors of proliferation networks will be to find common participation within organizations or with specific trafficking events. For this reason, only binary relations will be used between actors to represent the presence or absence of a tie.

b. Directed Ties

Just as relations between actors can be measured to accommodate various discriminators, they can also represent a directional tie that exists between actors. Directed or “bonded” ties are often used in advice or trust networks that display whom each actor goes to for advice or who they trust.

Since advice and trust are not necessarily reciprocal, they are considered to be

239 Robert A. Hanneman and Mark Riddle, Introduction to Social Methods, (Riverside, CA:

University of California, 2005), under "Chapter 3: Using Graphs to Represent Social Relations."

240 Ibid.

241 Ibid.

directed ties and are displayed on a graph with arrow heads “indicating who is directing the tie toward whom.”²⁴² Much like the decision to use only binary values to represent relations between actors of proliferation networks, the available data for each case study does not support the use of directed ties.

c. Simplex and Multiplex Relations

One of the inherent values of using social network analysis to describe complex illegal, or dark networks, is the ability to represent multiple relations between individual actors. Simplex relations “represent a single type of relation among actors” while multiplex relations display “more than one kind of relation.”²⁴³ The ability to graph multiplex relations will become instrumental in the discussion of proliferation networks that exhibit commonality between organizations involved in discrete trafficking events. For example, a freight forwarder that was established and subsequently coordinated logistics for multiple events will have multiplex relations between actors associated with that organization through association with each of the events.

d. Matrices

With very large networks, either containing a large number of actors or depicting many kinds of relations, graphs can become cluttered to the point that patterns are not easily discernable. In this case, matrices can be used to input social data into mathematical and computer tools that perform analytical functions. A matrix “is nothing more than a rectangular arrangement of a set of elements…described by the number of rows of elements and columns of elements that they contain.”²⁴⁴ The simplest matrix is binary and represents a tie between actors with a one and the lack of tie with a zero.

242 Robert A. Hanneman and Mark Riddle, Introduction to Social Methods, (Riverside, CA:

University of California, 2005), under "Chapter 3: Using Graphs to Represent Social Relations."

243 Ibid.

244 Ibid.

Bob Carol Ted Alice Bob -- 1 1 0 Carol 0 -- 1 0 Ted 1 1 -- 1

Alice 0 0 1 --

Table 2. Example of an Asymmetric Adjacency Matrix²⁴⁵

A matrix such as this represents the starting point for most network analysis, and “is called an ‘adjacency matrix’ because it represents who is next to whom in the ‘social space’.”²⁴⁶ The example provided in Table 2 depicts directed ties, the source of which is listed in the rows with the targets found in the columns. This matrix is, therefore, asymmetric as Bob chooses Carol, but Carol does not choose Bob.²⁴⁷

The terminology and principals presented thus far will be further elucidated in this chapter; they will form the basis for the subsequent analysis of weapons proliferation networks and their behavior as social networks. Using this construct will provide a point of departure to assess the current structure for regulating arms proliferation and provide the context for recommendations to stem the flow of small arms to the world’s conflict zones.