Two-Mode Data

A two-mode network, also known as an affiliation network, depicts relationships that connect entities of two distinct types. Examples are memberships of individuals in groups or participation in events by individuals. This entry describes typical uses of two-mode network data, sources from which they can be drawn, and some common approaches to studying them.

Two-mode network data include two different sets of nodes, one for each type of entity. Following convention, this entry uses the terms actors and events to distinguish between these node sets. All direct relationships in a two-mode network connect nodes that differ in type: neither actors nor events may be directly tied to one another. Ordinarily, however, they are indirectly linked—for example, when two individuals (actors) are co-members of a given group (event) or when two events have participants (actors) in common. In two-mode data, relationships usually are binary—either present or absent—although it is possible to add weights that reflect variations in relationship strength. Information about attributes of actors and/or events may supplement the relational data.

Some studies accord equal attention to the actors and the events. A high school social structure, for instance, could be represented by two-mode data on the participation of students (actors) in extracurricular activities (events). It might highlight patterns in how students affiliate with activities as well as in where both students and activities stand relative to one another.

Other applications place emphasis on entities of one type, say actors. Here, the indirect relations between actors mediated by their shared affiliations with events are of principal concern; these provide proxy measures of relationships within a one-mode projection network that links the actors. In this situation, the events serve to [Page 1749]connect the actors but are otherwise subordinated. A study of patterns in scientific collaboration may, for example, be based on a two-mode network reporting which scientists (actors) authored publications (events)—concentrating mainly on relationships among the scientists as reflected in their coauthorships, with little or no attention to particular publications.

Representations of Two-Mode Network Data

A two-mode network may be described as a set of subsets that include entities of one type, say actors; the subsets represent the other type (events). For example, consider the student members of five extracurricular groups in a small school; the groups are subsets of the 10 students:

• I (Service Club): {Casey, Kelly, Morgan, Riley, Taylor}
• II (World Cultures): {Blake, Parker, Taylor}
• III (Concert Band): {Drew, Noel}
• IV (Student Council): {Blake, Casey, Kelly, Noel, Parker}
• V (Ballroom Dancing): {Avery, Drew, Morgan, Noel}

Two-mode data are often presented in the form of an incidence matrix, in which rows index actors and columns events. With the usual binary data, entries of 1 indicate that an actor (e.g., student) is affiliated with an event (e.g., extracurricular group), while 0s indicate nonaffiliation. Table 1 displays the incidence matrix representation of the school data.

Table 1 Incidence Matrix for a Two-Mode Network
Extracurricular Group
Student	Service Club	World Cultures	Concert Band	Student Council	Ballroom Dancing
Avery	0	0	0	0	1
Blake	0	1	0	1	0
Casey	1	0	0	1	0
Drew	0	0	1	0	1
Kelly	1	0	0	1	0
Morgan	1	0	0	0	1
Noel	0	0	1	1	1
Parker	0	1	0	1	0
Riley	1	0	0	0	0
Taylor	1	1	0	0	0

Figure 1 Visualization of Incidence Matrix in Table 1

[Page 1750]Visualizations of two-mode network data include points for all actors and events and lines that symbolize their affiliations. Such displays distinguish actors and events using symbols with different shapes and/or colors. In the graph for the school data shown in Figure 1, black squares represent activities, while gray circles represent students.

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