Bipartite Networks

Bipartite networks refer to a specific kind of network in which the nodes (or actors) can be partitioned into two subsets based on the fact that no links exist between actors within each subset, but only between the two subsets.

Due to the partition of actors in two sets and the absence of relations within the parts, bipartite networks form a specific type of complete network, which differs from classic complete networks in a number of ways. One particular property includes the absence of three-cycles, or any higher order cycles of uneven number. As a result the smallest closed configuration is a four-cycle, i.e., a configuration where two nodes of one set (i and j) are both connected to two nodes of another set (k and l).

In practice, bipartite networks seem to be similar to two-mode networks, and sometimes bipartite networks are used interchangeably with two-mode or affiliation networks. However, theoretically bipartite and two-mode networks are clearly distinct, since in the former the focus of the research question is on all the actors in the two subsets, whereas in the two-mode network the focus is often on one of the two modes (subsets). Affiliation (two-mode) networks a priori define two clearly distinct kinds of actors (such as events and persons), and the relations involve persons attending these events, such as theater attendees, researchers working together on projects, or collaboration on articles. These are represented in an actor-by-event matrix, and the interest is generally on one of the two kinds of actors (modes).

Bipartite networks generally refer to one type of actor, which can be distinguished based on some characteristic or, alternatively, ad hoc based on the structure. The focus often lies on both subsets of actors at the same time. According to Stephen Borgatti and Martin Everett, “In general, bipartite networks are distinct from two-mode networks in the reasons for their structure, not in their resulting properties.” Hence, these are represented in an actor-by-actor matrix, where both subsets of actors are presented in both the columns and the rows. Nevertheless, two-mode networks can also be translated into a bipartite format by putting actors and events behind each other. That is why some will treat two-mode networks as a subset of all bipartite networks [Page 76](or a representation of bipartite), which has the same structure but is only theoretically distinct.

Dating relationships in a high school, where many of these links are exclusively between girls and boys, is an example of a bitartite network. In social network research, the centrality is analyzed for the two subsets of actors at the same time.