Breiger, 1974 is a classic in social network analysis. It offers a way of using group membership to show a) how people are connected by their shared affiliations and b) which groups are important to a collection of people.
The following notes are intended to offer a step-by-step process for assembling Breiger-type networks.
I will demonstrate the applicability of this approach to the history of psychology by illustrating each step using the example of first 10 presidents of the American Psychological Association and their university affiliations.
Before you get started, you need to download and install both the converter add-in for Excel and gephi.
A) Data Entry
1. In Excel, set up an array with persons as rows and groups (institutions, events, etc) as the columns
2. If an individual participated in a group, enter 1 in the appropriate cell. If not, 0
Each row is dedicated to an APA president and each column represents a university. This is a much simplified version of the history. For illustrative purposes, I have only included those institutions where more than one individual studied or taught. For example, Joseph Jastrow spent most of his career at the University of Wisconsin. However, no one else shared this connection. In this case, a shared institution does not necessarily mean a concurrently share institution, although given the time frame this was often the case.
B) Array Multiplication
3. Select the entire array (including labels) and copy
4. “Paste special” and select “transpose”
You can see that this table contains the same inform but has simply been inverted.
5. Cut and paste the appropriate labels. They should be the same vertically and horizontally. In other words, along the diagonal from the first cell there should be a line where the labels are identical
6. Highlight the area within the 2 axes created by the labels
7. In the formula bar, enter =MMULT(A2:B2,D1:E2); e.g. the range of the first array, the range of the second array
8. Instead of hitting enter, use ctrl+shift+enter
N.B.: Working with arrays in Excel is limited by the random access memory. If you get an error make sure the size of your array isn’t greater than what you version of excel can support.
In this table, people are connected to people with the number of connections (e.g. the number of shared institutions) appearing in the cell. For example Hall and Munsterberg have a connection to both Leipzig and Harvard. If you look at the cell at the intersection of Hall and Munsterberg (or Munsterberg and Hall) you’ll see 2
C) Converting an Array to an Edge List
9. Copy the new array (including labels) and open a new Excel document
10. Under Edit, “Paste special”: select “values”
11. Delete the values in the diagonal line where the same labels are identical
12. Under Tools, select matrix converter. In a series of pop up windows, it will ask you a number of questions.
13. For header rows: 1
14. For column rows: 1
15. For Field Name Row 1: Source
16. For Field Name Row 2: Target
18. Add a column labelled “type” and fill down either “directed” or “undirected” as appropriate
19. N.B.: The converter will count both of a tie’s appearances in the array (e.g. Hall’s connection to Munsterberg, and Munsterberg’s connection to Hall). This matters when calculating weighted degree in gephi, but the solution is pretty easy.
20. Create a new column labelled “weight.” Its value is the adjacent “data” column divided by 2 (e.g. = C2/2, = C3/2, = C4/2 etc.)
Your final table should look something like this:
21. You have not converted the array into an edge list compatible with gephi
22. Save the new excel document as a CSV (comma delineated) file
23. Open a new project in gephi
24. Go to the “Data Table” tab
25. Import your CSV document as an edge table. Gephi will ask you which columns you want to import. When importing, you should select the columns labelled “Source,” “Target,” “Type,” and “Weight.” You want to ignore the column labelled “data”
26. At this stage you can do all sorts of manipulations in Gephi such as getting the various measures of degree, adding labels to the nodes, and scaling them based on various measures.
Figure 1: People
This graph tells us some interesting things about the social structure of the early APA. William James seems fairly marginal (because he was only affiliated with Harvard). In some ways, this strikes the historian as wrong. James was the most famous psychologist in the United States and he wrote the field-defining textbook. This graph undoubtedly fails to capture the nature and extent of his considerable influence. However, historians have also long recognized that James’s pluralistic vision for psychology did not necessarily mesh well with the men pushing to organize and institutionalize the discipline. In this regard, the greater weighted degree of James McKeen Cattell followed by G. Stanley Hall and Joseph Jastrow (the epitome of the organization men in science) is unsurprising. See Ross, 1972; Sokal, 1990, 1992.
Figure 2: Groups
This graph illustrates which institutions loomed largest when it came to becoming an early APA president. What I find most interesting is that Leipzig (Wundt’s institution and the most iconic place in the rhetoric of the “new psychology”) has a high degree of centrality in the network but is not the most important place. Instead, having an affiliation with the short-lived philosophy department at the Johns Hopkins University mattered more when it came to becoming an APA president. For more about the culture of this department see Behrens, 2005; Green, 2007; Pettit, 2013. Furthermore, Columbia University in New York City became an important home for many of organized psychology early leaders.
Behrens, P. J. (2005). The Metaphysical Club at the Johns Hopkins University (1879–1885). History of Psychology, 8(4), 331–346.
Breiger, R. L. (1974). The Duality of Persons and Groups. Social Forces, 53(2), 181–190. doi:10.1093/sf/53.2.181
Green, C. D. (2007). Johns Hopkins’ First Professorship in Philosophy: A Critical Pivot Point in the History of American Psychology. American Journal of Psychology, 120, 303–323.
Pettit, M. (2013). The Science of Deception: Psychology and Commerce in America. University of Chicago Press.
Ross, D. (1972). G. Stanley Hall: The psychologist as prophet. Chicago: University of Chicago Press.
Sokal, M. M. (1990). G. Stanley Hall and the institutional character of psychology at Clark 1889–1920. Journal of the History of the Behavioral Sciences, 26, 114–124.
Sokal, M. M. (1992). Origins and early years of the American Psychological Association, 1890–1906. American Psychologist, 47(2), 111–122.