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Mathematics LibreTexts

12: Positions and Roles - The Idea of Equivalence

  • Page ID
    7720
  • [ "article:topic-guide", "authorname:rhanneman" ]

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    • 12.1: Introduction to the Idea of Equivalence
      Now we are going to turn our attention to somewhat more abstract ways of making sense of the patterns of relations among social actors: the analysis of "equivalence classes". Being able to define, theorize about, and analyze data in terms of equivalence is important because we want to be able to make generalizations about social behavior and social structure. That is, we want to be able to state principles that hold for all groups, all organizations, all societies, etc.
    • 12.2: Approaches to Network Positions and Social Roles
      Because "positions" or "roles" or "social categories" are defined by "relations" among actors, we can identify and empirically define social positions using network data. In an intuitive way, we would say that two actors have the same "position" or "role" to the extent that their pattern of relationships with other actors is the same. But, there are a couple things about this intuitive definition that are troublesome.
    • 12.3: Defining Equivalence or Similarity
      There are many ways in which actors could be defined as "equivalent" based on their relations with others. For example, we could create two "equivalence classes" of actors with out-degree of zero, and actors with out-degree of more than zero. Indeed, a very large number of the algorithms we've examined group sets of actors into categories based on some commonality in their positions in graphs.
    • 12.E: Positions and Roles - The Idea of Equivalence (Exercises)
    • 12.S: Positions and Roles - The Idea of Equivalence (Summary)
      The three types of equivalence (structural, automorphic, and regular) have progressively less strict definitions of what it means for two actors to be "equivalent". And, as we make the definitions less strict (which is not the same as making them less precise!), we are able to understand social networks at increasing levels of abstraction.