Equivalence and blockmodeling in the analysis of social networks

Structural equivalence builds on a strict definition of similarity of ties, treating as equivalent only such nodes that have the same ties to the same other nodes. Regular equivalence works with looser criteria and better corresponds with both the theoretical and the intuitive notions of role; this, however, is outweighed by the absence of a unique regular-equivalent solution within a network and by the difficulty to process networks with undirected ties. Regular-equivalent nodes are such that have ties to other mutually equivalent nodes. I present examples to demonstrate the differences between both definitions.

In the following section, I discuss measurement of similarity between the different nodes’ profiles of ties (e.g., correlation and Euclidean distance) and possible uses of the standard statistical methods of cluster analysis and multidimensional scaling to detect equivalent classes of nodes within networks. After pointing to the weaknesses of these techniques in network data analysis, I present blockmodeling as a method designed specifically to identify roles and positions within networks. I schematize the blockmodeling procedure and present its basic terms before comparing classic inductive blockmodeling, which is primarily fit for the purposes of exploration and network reduction, with deductive generalized blockmodeling, which is applicable in testing hypotheses about basic structural characteristics of a network. I bring attention to the strengths and weaknesses of both approaches. Relatedly, I present an application of blockmodeling especially for the purposes of simplified network representation, comparing structural patterns across networks, and testing structural theories.

In the following section, I demonstrate specific blockmodeling algorithms based on both structural equivalence (CONCOR and Tabu Search optimization) and regular equivalence (REGE and Tabu Search optimization). Then I verify the adequacy of their resulting assignment of positions to nodes using eta coefficient, Q modularity and correlation of the ideal blocked and the empirical adjacency matrices. In the concluding section, I demonstrate the entire blockmodeling procedure on an empirical case of a small network with undirected ties using the UCINET software tool, including interpretation of results. Finally, I reflect the contemporary position of blockmodeling among leading research approaches in SNA, referring to other empirically oriented studies that demonstrate the broad applicability and utility of position analysis.

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