Structural Equivalence

Structural equivalence (sometimes called streq) is one of the most important concepts in social network analysis and is related to a broader theoretical context in the field. It has faced some criticisms, which has stirred up some recurring debates. The concept of structural equivalence was first proposed by sociologists François Lorrain and Harrison White in 1971, even though they both recognized that the concept was already present, at least implicitly, in pre-existing mathematical literature. In short, structural equivalence can be defined in the following way: two actors in a network are considered structurally equivalent if they share the exact same set of ties to third-party actors. In other words, two actors are structurally equivalent if they are connected, and not connected, to the same actors.

For example, consider a network constituted of six actors, A, B, C, D, E, and F (see Figure 1). In this network, exclusively constituted of undirected ties—which are reciprocal—A is connected to D and E. B is connected to E and F. C is connected to D and E. A and C are thus structurally equivalent because they are both connected to D and E and not connected to the other actors. However, A and B are not structurally equivalent because while they are both connected to E, B is connected to F, while A is not. A similar reasoning can be made for directed, that is, nonreciprocal, ties. In other words, two actors are structurally equivalent if they share the exact same profile of ties to others. Structurally equivalent actors need not be connected to each other.

Figure 1 Illustration of Structural Equivalence for Six Actors: A and C Are Structurally Equivalent

Structural equivalence is more than an abstract concept and can be grasped intuitively. It can be found in many everyday life settings, such as in kinship, at work, or in markets. Siblings of the same gender can, to some extent, be considered structurally equivalent. Employees of a given firm who perform the same tasks or occupy the same hierarchical position with the same subordinates and the same managers can be considered approximately structurally equivalent. Firms that share suppliers and sell to the same customers are structurally equivalent. An important idea is that even though two actors are structurally equivalent, it does not mean they are equivalent in other ways. Consider two brothers, who share the same set of relations to their kin. These brothers are structurally equivalent as far as their kinship relationships are concerned. However, they can have different attributes, such as different academic degrees or tastes. In this regard, they are structurally equivalent, but not socially equivalent. Structural equivalence is concerned with the overall structure of a network, not the attributes of the actors. In concrete empirical contexts, however, perfect structural equivalence is hard to find, and actors can be considered structurally equivalent if they share similar but not identical patterns of ties. This looser definition of structural equivalence is used when measuring the concept and identifying structurally equivalent actors in a network.