Triads

A basic element of social network theory and analysis is the dyad, or pair of actors who may or may not share a social relation with one another. A triad is a set of three actors, which also consists of three dyads. In his seminal work, Georg Simmel argued that triads are a fundamental unit of sociological analysis. He argued that three actors in a triad may allow qualitatively different social dynamics that cannot be reduced to individuals or dyads. For example, among three parties A, B, and C, party A may have a dyadic relation to C but also may have an indirect relation to C through B. Party B may then alter the strength or the nature of the relation between A and C, such as solidifying an alliance or mediating a conflict. If A and C do not interact directly, party B may broker a transaction between them and may derive power from this intermediary position.

A principal interest in the study of triads is the phenomenon of transitivity. A triad is transitive if when there is a tie from A to B and from B to a third party C, there is also a tie from A to C. If the A–B and B–C ties both exist but A is not tied to C, then the triad is intransitive. (This condition must be checked for any assignment of the labels A, B, and C to the three parties.) Transitivity is typically studied for directed relations, where a tie from A to B (denoted A→B) is directional and does not imply the same relation from B to A. For triads in directed networks, if the A→B and B→C ties both exist but A→C does not, then the triad is intransitive.

Figure 1 Illustrations of Intransitive Triads: Undirected (left) and Directed (right)

Some directed relations have a pervasive tendency toward transitivity: if A dominates B and B dominates C, then A is also likely to dominate C. Some undirected relations also tend to be transitive, as represented by the adage, “a friend of a friend is a friend.” Triads for some other relations—notably romantic ties between lovers—are overwhelmingly intransitive.

Simmel also argued that triads may serve as an analytical foundation for understanding larger social groups. Researchers have thus described networks by examining the distribution of relations at the triadic level, enumerating all qualitatively distinct triadic configurations. This “triad census” has been used to observe an overall tendency toward sociability, hierarchy, or transitivity in social networks and formed an early foundation for statistical network analysis.