Constructing blockmodels: How and why

It is proposed that the distinctive and advantageous feature of CONCOR is that it solves what is initially presented as a combinatorial problem by representing the problem as a continuous one (analysis of correlation matrices), and it is predicted that the fairly crude empirical approach of CONCor will be supplanted by more powerful procedures within this same class.

Abstract

Blockmodel approaches to network analysis as developed by Harrison White are shown to fall in a broader class of established data analysis methods based on matrix permutations (e.g., clique detection, seriation, permutation algorithms for sparse matrices). Blockmodels are seen as an important generalization of these earlier methods since they permit the data to characterize their own structure, instead of seeking to manifest some preconceived structure which is imposed by the investigator (e.g., cliques, hierarchies, or structural balance). General algorithms for the inductive construction of blockmodels thus occupy a central position in the development of the area. We discuss theoretical and practical aspects of the blockmodel search procedure which has been most widely used (CONCOR algorithm). It is proposed that the distinctive and advantageous feature of CONCOR is that it solves what is initially presented as a combinatorial problem (permutations of matrices to reveal zeroblocks) by representing the problem as a continuous one (analysis of correlation matrices). When this representation strategy receives further development, it is predicted that the fairly crude empirical approach of CONCOR will be supplanted by more powerful procedures within this same class.