Chapter 12 Network positions and social roles: The idea of equivalence 1

Contents 12.1 Introduction 12.2 Approaches to network positions and social roles 12.3 Defining equivalence or similarity Structural equivalence Automorphic equivalence Regular equivalence 12.4 Summary 2

12.1 Introduction patterns in the overall structure (connectedness, density) the embeddedness of each actor (geodesic distances, centrality) “sub-structures,” or groupings of actors that are closer to one another than they are to other groupings.(“cliques” “blocks” and “bridges”) make generalizations about social behavior and social structure actors not as individual unique persons (which they are), but as examples of categories -- sets of actors who are, in some defined way, "equivalent.“  [Discussion : definition of “category”] 3

definition of a category, “social role”, “social position” depends upon the similarities of the patterns of relations among actors and its relationship to another category, rather than attributes of actors. it is the relation between occupants of the two role that defines the meaning of the roles [E.g., meaning of "worker" depends upon a capitalist -- and vice versa. (in this case, as Marx would say, a relation of exploitation) ]  [Discussion : the definition of “product category”, “student”] 4

the social roles or positions are defined by regularities in the patterns of relations among actors, not attributes of the actors themselves. “attributes of individuals”can be thought of as short- hand labels for patterns of relations 5

12.2 Approaches to network positions and social roles First, what relations to we take into account, among whom, in seeking to identify which actors are similar and which are not? Second, what do I mean that actors who share the same position are similar in their pattern of relationships or ties? it is all depends upon the purposes of our investigation. 6

12.3 Defining equivalence or similarity Structural equivalence Automorphic equivalence Regular equivalence 7

Structural equivalence if they have the same relationships to all other nodes. two actors must be exactly substitutable  [Discussion : how many structural equivalence classes? ] "strongest" form: completely substitutable 8

Automorphic equivalence [E.g. a franchise group of hamburger restaurants] actor B and actor D -not structurally equivalent (same boss, but not the same workers) -automorphic equivalence (same boss and each has exactly two workers) the faces are different, but the structures are identical: all of the distances among all the actors in the graph would be exactly identical.  [Discussion : how many automorphic equivalence classes?] 9

five automorphic equivalence classes: {A}, {B, D}, {C}, {E, F, H, I}, and {G} The idea of automorphic equivalence is that sets of actors can be equivalent by being embedded in local structures that have the same patterns of ties -- "parallel" structures. less strict definition -reduced the number of classes. 10

Regular equivalence same profile of ties with members of other sets of actors that are also regularly equivalent. [E.g., “two mothers”] -not structurally equivalent(not have ties to the same husband, or the same children or in-laws) -not be automorphically equivalent(different mothers may have different numbers of husbands, children, and in-laws) -regularly equivalent(same relationships with some member or members of another set of actors)  [Discussion : how many regular equivalence classes?] 11

three regular equivalence classes : {A}, {B, C, D}, {E, F, G,H, I} {E, F, G,H, I} -no tie with any actor A -each has a tie with an actor in the second class (either B or C or D); -has an identical pattern of ties with actors in the other classes. {B, C, D} -have a tie with actor A -each have a tie with a member of the third class. {A} -a tie to at least one member of class two, and no tie to any member of class three. not necessarily fall in the same network positions or locations with respect to other individual actors; rather, they have the same kinds of relationships with some members of other sets of actors. 12

12.4 Summary Structural equivalence -“strongest” form(same ties/ same position in a structure/same sets of constraints and opportunities) Automorphic equivalence -a bit more relaxed(not be tied to the same others, but they are embedded in the same way in the larger structure; same distance from other sets of actors) -parallel or substitutable sub-structures (rather than substitutable individuals). Regular equivalence -it gets at the notion of which actors fall in which social roles, and how social roles (not role occupants) relate to one another. progressively less strict definitions-increasing levels of abstraction.  [Discussion ： implication in marketing] 13

Recommendation Harkola, J., & Greve, A. (1995). Diffusion of technology: Cohesion or structural equivalence? Academy of Management Journal, 422. The goal of a study was to investigate the diffusion of a construction site technology in a Japanese firm. Comparing diffusion of technology by cohesion and structural equivalence shows that cohesion is effective in higher density networks, whereas structural equivalence affects diffusion in low density networks as a mimetic process. A behavioral argument regarding the influence of structural equivalence focuses on imitation and reference groups. People act as they believe people in their position should act. It seems that members of the different study groups came to different conclusions about the utility of the technology and then acted appropriately, based on their position in the social network. 14

Thank You! 15