Two-Mode Networks

Most social networks consist of only one type of node, or type of observational unit. For example, students may be friends with other students of the same school, or [Page 887]employees may work with other employees in the same corporation. These kinds of social networks are called one-mode networks. Figure 1 shows a simple one-mode social network in which all nodes are of the same type. A characteristic of one-mode networks is that every node can, in principle, be connected to every other node. For instance, each student can be friends with all the other students in the same school, or each employee works with all other employees in the same corporation. The reference to the word mode comes from the language of matrix algebra, in which a mode refers to a distinct set of entities in a matrix.

Figure 1 Example of a One-Mode Social Network

Many social networks, however, are two-mode networks (also known as affiliation or bipartite networks), or networks with two or more types of nodes. For example, sociologists have examined nation-states interlinked via international organizations, scientists connected to other scientists through coauthorship of research articles, and business executives linked to other executives through joint memberships on corporate boards. Figure 2 shows a simple two-mode network, in which one type of node is indexed by letters, and another type is indexed by numerals. In networks with two distinct types of nodes, relationships can only occur between different types of nodes. Thus, in contrast to one-mode networks, it is impossible for every node to be connected to every other node. For example, although scientists can coauthor research articles, and research articles can be coauthored by scientists, scientists cannot coauthor other scientists, and research articles cannot coauthor other research articles. For example, in Figure 2, this means that nodes one and two can only be connected through the intermediate node A and not directly linked.

Figure 2 Example of a Two-Mode Social Network

Because of the constraints imposed by modeling two distinct types of nodes, there are few direct measures of two-mode social networks. Instead, two-mode networks are most commonly analyzed through conversion into a one-mode network. This approach is also called projection, since it is mathematically equivalent to projecting a two-dimensional object onto a one-dimensional object. With conversion, the analyst simply selects one of the two nodes and collapses the network on that node. Technically, this is usually accomplished by either pre- or postmultiplying the matrix by its transpose. After conversion, typical network analytic techniques are applied. For instance, referring to Figure 2, if the analyst selects the nodes indexed by numerals, the resultant network will be that shown in Figure 1. However, if the nodes indicated by letters are selected, the resultant network will look like that shown in Figure 3. In both cases, the two-mode network is collapsed into a one-mode network.

Figure 3 Example of a Two-Mode Network After Conversion

Although widely used, conversion entails some difficult theoretical and methodological issues. Most obviously, there is the difficulty of selecting which node to retain after conversion. Typically, the most [Page 888]theoretically interesting node is selected, but in some contexts, this may not be obvious. Another problem is that merely collapsing a two-mode network into a one-mode network ignores that some nodes may be more connected than others. One solution is to weight the ties after conversion, with weights proportional to the number of ties between the nodes.

...