12 - Extending Generalized Blockmodeling

Summary

In our concluding chapter, we step back from the details of specific analyses and examine the overall framework within which these analyses were conducted. In Chapter 6, we distinguished conventional and generalized blockmodeling and stressed fundamental differences between the two approaches. Chapters 6–11 contain a variety of blockmodels fitted with the generalized blockmodeling framework. Here, we pursue some of the implications stemming from the use of generalized blockmodeling methods.

BLOCK TYPES

One key feature in the development of generalized blockmodeling is the translation of equivalence ideas into a corresponding set of ideal block types. For structural equivalence, the two ideal block types are null and complete. For regular equivalence we added the regular (one-covered) block type. Empirically, rather than focus on types of equivalence per se, we focused on the block types. This has the benefit, realized in the materials in Chapters 6–11, of permitting a potentially unending way of generalizing blockmodels and motivates the title for this book. Once we are free to specify additional block types, we are freed from having to conform to one or two particular definitions of equivalence. As a result, we are able to specify new types of blockmodels based on the new block types. The expansion of block types and blockmodel types can proceed both on substantive and technical foundations.

In the initial presentation of new block types in Chapter 7, row-regular blocks and column-regular blocks are natural generalizations of regular blocks that were useful block types for the TI example and the baboon grooming network. The row-function and column-function blocks were blocks that were specified more on technical grounds.