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Pajek | Ineffective Elective Affiliations

I have come to an impasse in my reading of the Pajek manual and hope that someone will be able to point me to the exit of this tangled Webs we weave …

Chapter 5 of the Pajek social networking textbook is uncharacteristically less than a model of clarity when it comes to 2-mode networks, I am finding.

The problem at hand is to analyze 2-mode relationships as relations between two or 1-mode relationships.

The example given — one that interests me a great deal in this work I work on during downtime — is a network of interlocking directorates among late-19th century Scottish heavy industry players.

I propose that this sort of analysis would be informative when attempting to unravel contemporary relations among industry, government and the «third sector». These sorts of structural ties can reflect hidden or modestly soft-peddled synergies that should be useful to the Kremlinologist of such masters of the postmodern corporation as Bill Gates and the boys who brought you eBay and the original 1984 Apple toaster oven, along with relative newcomers to the game of billionaire IPO.

SourceWatch would be a natural client for this sort of analysis, although it tends to be too far behind the constant hubbub of musical chairs to be useful. I say that with all due respect and as someone who admittedly is complaining without contributing toward a solution.

In my defense, please note my efforts to master concept mapping with CMaps, above,and adapt it to the stated end. Above, rough sketch of interlocks inside the State Department’s innovation policy commission and board of broacasting governors.

Now, here is where I got hung up as I wandered the forking paths of the textbook: on the alpha and omega of the 2-mode network, which divides the network into two partitions, in this case «actors» and «events». This should enable us to draw and label the lines binding events with the Node ID of actors stored in a separate partition.

The problem is actually a simple one. I followed the note on how to evoke the Partitions > Second From First technique and found that the software did not perform as advertised.

  1. Net>Partitions>Degree>Input
  2. Partitions>Extract Second from First

I do not understand which target this command is supposed to be performed on.

The textbook says,

Imagine, for example, that we want to know the degree of the firms in the two-mode network, which is equal to the number of their multiple directors (the size of the events). We compute the degree in the usual manner with the Degree>Input command in the Net>Partitions submenu.

I assume we mean the degree of the 2-mode network, but when I issue this command, a new item in the toolbar Partitions menu is not created.

The partition created by this command does not distinguish between the firms and the directors, so we must extract the firms from it.

We select the degree partition as the first partition in the Partitions menu to extract the firms.

I believe the degree partition should read as shown. Next, on the other hand, we need to issue Partitions>Second from First, which is to say, the «affiliation» net from the «degree» net.

Next, we select the affiliation partition as the second partition in the Partitions menu because it identifies the firms within the network.

The basic problem is that when the network .net file was loaded, an affilate partition was not automatically created.

Finally, we extract class 1 (the firms) of the affiliation partition from the degree partition with the Partitions>Second from First command.

The following does not occur.

When Pajek opens a data file in this format, it automatically creates a partition that distinguishes between the first subset of vertices (class 1) and the second (class 2). This partition is labeled “Affiliation partition” in the Partition drop-down menu.

Not. The data file referred to, I find, after some hair-tearing, is not formatted properly

This seems to be a formatting error.

The textbook calls for the first line of the file to read as follows:

*Vertices 244 109

Shall we try that? Loading the revised data file, we receive a warning.

No partition is created.

Finally, loading the .paj file instead of the .net file does create the «affiliation partition».

Can we now perform the extraction we initially set out to do?

Net > Transform > 2-Mode to 1-Mode

This command does not respond. It should extract a ROW and COL subset from the original network according to the bipartite separation of Agents — board members — and Events — board meetings.

I have now successfully completed the analysis explained in the book — Extact Second from First — but I find myself with a new problem:  Now

Net > Transform > 2-Mode > Row, Column

is not responding.

Well, I have made myself out to be a right idiot indeed with the these meanderings. Sometimes, thought, the blog makes a handy repository of devilish details such as these, for recollection down the road.

Eventual Solution

I was right: the .net and .paj files for the network contained an error. The first line read

*Vertices 244

iistead of

*Vertices 244 108

for number of vertices and number of vertices in the first partition …

With that, I am finally able to reproduce the example given: a 2-node network of actors — board members — and events — board seatings.

Following instructions, I extracted the degree partition of the overall network, then extracted the 2-mode partition with

Partitions > Second from First

Next — and the text could have made this more explicit — I extract Partition 2 and draw the result.

As you can see, the result is a network of firms connected by shared directors, whose names appear as edge labels.

Extracting Partition 1, we get a network of directors connected by seats on the same boards.

We can now, for example, visualize the most connected of the board directors studied.

Spheres of influence can be detected, with some caveats about the meaning of ties in distinct situations.

Gephi will output an adjacency matrix usable in yEd, after first being converted to Microsoft Excel in Open Office Calc.

This exercise was a bit frustrating — I only got a 750 on my math SATs all those centuries ago — but also educational and worth the trouble.