Example Use Case: Fortune 100 Boards of Directors :: SAS/GRAPH(R): Network Visualization Workshop 2.1 User's Guide

Introduction to the Boards of Directors Example

This example describes how to use SAS/GRAPH Network Visualization Workshop to investigate relationships among boards of directors of Fortune 100 companies circa the year 2001. The goal is to identify influential board members and uncover relationships among companies that share common directors.

The data for this example was obtained directly from various corporate Web sites.

A visualization of this data is shown in the following figure. The blue nodes in the network represent directors or chief executive officers (CEOs), and the red nodes represent corporations. Each arc links a director to a corporation. The red arcs link CEOs and their corporations, while green arcs link general directors and their corporations.

Boards of Directors Network

Open the Boards of Directors Project

To open the project:

Open the BoardOfDirectors.nvw project, which is located in the Samples\Projects subdirectory of your installation.

This project automatically loads the node and link data sets. The project also loads the hierarchical network graph that you examine in this example.
Select DataEdit Attributes. The Edit Data Attributes dialog box opens. Set or make sure that the attributes have been set as indicated here:

Link Attributes

Select INDIVIDUAL from the From list box.

Select CORPORATION from the To list box.

Select CEO from the Color list box.

Node Attributes

Select NAME from the ID list box.

Leave the Shape list box set to <None>.

Select TYPE from the Color list box.

Select FULL_NAME from the Label list box.
Select ViewStyleDefault to use the Default style that is seen in this example.

About the Data Used in the Example

The data for this example is contained in two data sets: a node data set (bdnodes.sas7bdat) and a link data set (bdlinks.sas7bdat).

The following figure shows a portion of the node data set:

Node Data Set (bdnodes.sas7bdat)

The following table summarizes the variables in this data set:

Node Variables for the Boards of Directors Sample

Variable	Description
NAME	Lists the names of individuals and corporations. This variable serves as the Node ID variable in the Edit Data Attributes dialog box.
FULL NAME	Lists the full names of individuals and corporations.
CATEGORY	Classifies the corporations and individuals. This variable also indicates which individuals are CEOs.
TYPE	Indicates whether the node is an individual (I) or a corporation (C). This variable also determines the colors of the node markers. This variable serves as the Color variable in the Edit Data Attributes dialog box and, therefore, determines node colors.
NUMBER_OF_BOARDS	Represents the number of boards of which an individual is member. For a corporation, this variable gives the size of the corporation's board.
REVENUES	Provides the revenues of corporations. For individuals, this value is ignored.

The following figure shows a portion of the link data set:

Link Data Set (bdlinks.sas7bdat)

The following table summarizes the variables in this data set:

Link Variables for the Boards of Directors Sample

Variable	Description
INDIVIDUAL	Serves as the From variable that originates the link.
CORPORATION	Serves as the To variable that terminates the link.
BOARD CHAIRMAN	Indicates whether the individual is (1) or is not (0) the board chairman of the corresponding corporation.
CEO	Indicates whether the individual is (1) or is not (0) the chief executive officer of the corresponding corporation. This variable serves as the Color variable in the Edit Data Attributes dialog box and, therefore, determines link colors.
NUMBER OF BOARDS	Indicates how many boards the individual is a member of.
BOARD SIZE	Indicates the size of the board.

Note: The From Index and To Index variables are not shown in the figure or included in the previous table. These variables are automatically generated, zero-based indexes into the node data set.

Identifying Corporate Bonds

The density of the network makes it difficult to detect patterns involving individuals and corporations of interest, such as the individuals who sit on multiple boards. You can use a statistical graph in combination with the network graph in order to produce a subnetwork of the data. The result is a network graph that shows individuals who sit on four or more different boards.

Directors on Four or More Boards

In this graph, you can see that nine individuals sit on four or more different boards. There are nine blue nodes that connect with four or more red nodes. Two of these directors sit on five boards, and one director sits on six different boards. These patterns suggest possible relationships between companies that might not be readily apparent.

The following steps describe how to create this graph:

Click the link data table to activate it.
Create a histogram using the GraphsHistogram menu option. Select NUMBER_OF_BOARDS as the X variable. Leave the default <Frequency> for the Y variable.
In the histogram, select the bars with an X value greater than or equal to four. Hold the CTRL key to make multiple selections. Alternatively, drag a rectangle around the bars that you want to select.

The following display shows the histogram with the bars selected:

Histogram with Some Bars Selected
Select Tools Interactive Zoom. Then click the network graph to zoom in on the graph.
If you want to see the names of the CEOs and corporations, select ToolsLabel, and then click the blue nodes in the network graph.

Detecting Interlocks

According to Investor Responsibility Research Center’s (IRRC) definition, there is an interlock when two CEOs sit on the boards of each other’s companies. Interlocks are often viewed with a degree of suspicion; therefore, it's important to identify interlocks in the network. The subnetwork of interlocks is shown in the following figure. Here you can see there are two interlocks:

Sanford Weill, the CEO of Citigroup, sits on the boards of AT&T and United Technologies.
Michael Armstrong and George David, the CEOs of AT&T and United Technologies, respectively, sit on the board of Citigroup.

Subnetwork of Interlocks

A quadrilateral consisting of two CEOs and two corporations represents an interlock. The interlocks can be detected by finding the quadrilaterals in this much sparser subnetwork.

You can use a statistical graph and the local selection feature to filter the data in the network graph.

The following figure shows the result of using a bar chart with local selection mode to parse the visualized data. In this graph, links are visible only for CEOs who sit on two or more boards.

CEOs Who Sit on Two or More Boards

The following steps describe how to create this graph in the BoardOfDirectors.nvw project:

Close any statistical graphs that you have open. Keep the single network graph open.
Click the node data table to activate it.
Create a bar chart using the GraphsBar Chart menu option. Select CATEGORY as the category variable. Leave the default values in the other fields.
In the bar chart, select the bar for CEO.
Select DataSelection ModeLocal. An icon is displayed in the upper left corner of each graph. The icon for the network graph () indicates that the graph has an observer-union role.
Select the network plot. Then click the arrow in the icon and select the observer-intersection icon (). The graph now has an observer-intersection role.
Select all observations in the node data table.

Tip
You can click the table and then press CTRL-A to select all observations.
In the bar chart, press CTRL and select the bar for Other.

Bar Chart with CEO and OTHER Selected
Click the link data table to activate it. Then, create a histogram using the GraphsHistogram menu option. Select NUMBER_OF_BOARDS as the X variable. Leave the default <Frequency> for the Y variable.
In the histogram, select the bars for the numbers greater than or equal to two.

Histogram with Number of Boards Greater than Two
Select Tools Interactive Zoom. Then click the network graph to zoom in on the graph.
Select Tools Pan. Then click and drag the network graph so you can focus on the portion that contains the quadrilateral.
If you want to see the names of the CEOs and corporations, select ToolsLabel, and then click the blue nodes in the network graph.

In summary, this example shows how to use SAS/GRAPH Network Visualization Workshop to identify relationships between directors and the boards on which they sit. You first identified individuals who sit on four or more different boards. Then you identified CEOs who sit on the boards of each other’s companies.