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Mathematics LibreTexts

13: Measures of Similarity and Structural Equivalence

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    In this rather lengthy chapter we are going to do three things. First, we will focus on how we can measure the similarity of actors in a network based on their relations to other actors.Second, we will very quickly look at two tools that are very commonly used for visualizing the patterns of similarity and dissimilarity/distance among actors. Third, we will examine the most commonly used approaches for finding structural equivalence classes.

    • 13.1: Introduction to Measures of Similarity and Structural Equivalence
      The whole idea of "equivalence" that we discussed in the last chapter is an effort to understand the pattern of relationships in a graph by creating classes, or groups of actors who are "equivalent" in one sense or another. All of the methods for identifying such groupings are based on first measuring the similarity or dissimilarity of actors, and then searching for patterns and simplifications.
    • 13.2: Measuring Similarity/Dissimilarity
      We can be a lot more precise in assessing similarity if we use the matrix representation of the network instead of diagrams. This also lets us use the computer to do some of the quite tedious jobs involved in calculating index numbers to assess similarity.
    • 13.3: Visualizing Similarity and Distance
      It is often useful to examine the similarities or distances to try to locate groupings of actors (that is, larger than a pair) who are similar. By studying the bigger patterns of which groups of actors are similar to which others, we may also gain some insight into "what about" the actor's positions is most critical in making them more similar or more distant. Two tools that are commonly used for visualizing patterns of relationships among variables are also very helpful in exploring social net
    • 13.4: Describing Structural Equivalence Sets
      One very useful approach is to apply cluster analysis to attempt to discern how many structural equivalence sets there are, and which actors fall within each set. We will examine two more common approaches - CONCOR, and numerical optimization by tabu search.
    • 13.S: Measures of Similarity and Structural Equivalence (Summary)
      In this chapter we have discussed the idea of "structural equivalence" of actors, and seen some of the methodologies that are most commonly used to measure structural equivalence, find patterns in empirical data, and describe the sets of "substitutable" actors.  Structural equivalence of two actors is the degree to which the two actors have the same profile of relations across alters (all other actors in the network).

    13: Measures of Similarity and Structural Equivalence is shared under a not declared license and was authored, remixed, and/or curated by Robert Hanneman & Mark Riddle.