Examples of structuralism in the following topics:
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- This chapter and the next are concerned with the ways in which networks display "structure" or deviation from random connection.
- In the current chapter, we've approached the same issue of structuring from the "top-down" by looking at patterns of macro-structure in which individuals are embedded in non-random ways.
- The tools in the current chapter provide some ways of examining the "texture" of the structuring of the whole population.
- In the next chapter we will focus on the same issue of connection and structure from the "bottom-up. " That is, we'll look at structure from the point of view of the individual "ego."
- Taken together, the approaches in chapters 8 and 9 illustrate, again, the "duality" of social structure in which individuals make social structures, but do so within a matrix of constraints and opportunities imposed by larger patterns.
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- Structural equivalence is easy to grasp (though it can be operationalized in a number of ways) because it is very specific: two actors must be exactly substitutable in order to be structurally equivalent.
- In figure 12.1 there are seven "structural equivalence classes."
- E and F, however, fall in the same structural equivalence class.
- Finally, actors H and I fall in the same structural equivalence class.
- Actors that are structurally equivalent are in identical "positions" in the structure of the diagram.
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- Formal structure of an organization or group includes a fixed set of rules for intra-organization procedures and structures.
- The formal structure of a group or organization includes a fixed set of rules of procedures and structures, usually set out in writing, with a language of rules that ostensibly leave little discretion for interpretation.
- When attempting to create a formal structure for an organization, it is necessary to recognize informal organization in order to create workable structures.
- Tended effectively, the informal organization complements the more explicit structures, plans, and processes of the formal organization.
- A formal organization is a fixed set of rules of intra-organization procedures and structures.
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- The kind of equivalence expressed by the notion of automorphism falls between structural and regular equivalence, in a sense.
- Structural equivalence means that individual actors can be substituted one for another.
- Automorphic equivalence means that sub-structures of graphs can can be substituted for one another.
- The notion of structural equivalence corresponds well to analyses focusing on how individuals are embedded in networks -- or network positional analysis.
- Still, the search for multiple substitutable sub-structures in graphs (particularly in large and complicated ones) may reveal that the complexity of very large structures is more apparent than real; sometimes very large structures are decomposable (or partially so) into multiple similar smaller ones.
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- Structural equivalence is the most "concrete" form of equivalence.
- Two actors are exactly structurally equivalent if they have exactly the same ties to exactly the same other individual actors.
- Pure structural equivalence can be quite rare in social relations, but approximations to it may not be so rare.
- Commonly we would say that two actors who are approximately structural equivalent are in approximately the same position in a structure.
- Two actors may not be tied to the same others, but if they are embedded in the same way in the larger structure, they are equivalent.
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- Two actors that are structurally equivalent have the same ties to all other actors -- they are perfectly substitutable or exchangeable.
- There are a several approaches for examining the pattern of similarities in the tie-profiles of actors, and for forming structural equivalence classes.
- 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.
- A very useful approach to understanding the bases of similarity and difference among sets of structurally equivalent actors is the block model, and a summary based on it called the image matrix.
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- In this section 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).
- Exact structural equivalence is rare in most social structures (one interpretation of exact structural equivalence is that it represents systematic redundancy of actors; which may be functional in some way to the network).
- The first step in examining structural equivalence is to produce a "similarity" or a "distance" matrix for all pairs of actors.
- And, structural analysis, is primarily concerned with the more general and abstract idea of the roles or positions that define the structure of the group -- rather than the locations of specific actors with regard to specific others.
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- Which studies used the ideas of group sub-structures?
- Are there sub-structures within the kinship group of which you are a part?
- How is the population of Riverside divided into sub-structures?
- Are the nations in the world system divided into sub-structures in some way?
- How might the sub-structures in your real world case be described using the formal concepts (are the sub structures "clans" or "factions" etc.).
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- This chapter is about the kinds of "data structures" that network analysts work with most frequently, and some of the most common kinds of transformations and manipulations of these structures.
- A "data structure" is simply the way in which information is recorded.
- It is possible, for a data structure or data object to have more than two dimensions.
- Network analysts work with a variety of data structures.
- Different questions require different data structures.
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- How are network roles and social roles different from network "sub-structures" as ways of describing social networks?
- Actors who are structurally equivalent have the same patterns of ties to the same other actors.
- Did any studies used the idea of structural equivalence or network role?
- How many sets of structurally equivalent actors are there?
- Describe the structural equivalence and regular equivalence sets in a line network.