Block structures of automorphism groups of social relations

Abstract

This paper expands the concept of “block”, as in “blockmodeling”, by relating it to the “blocks” of permutation groups. Crucial to this development is the idea of graph automorphism, which captures the essence of “regular equivalence” in a way that allows the flexibility of the group block concept. Blocks, unlike regular or structural equivalence classes, are not disjoint, allowing overlapping and hierarchical structures to be described. One of the main application of these techniques is to “crack” a disappointingly small number of orbits (say one or two) found in highly symmetric graphs into a richer block structure.