Generalized blockmodeling of sparse networks

Abstract

The paper starts with an observation that the blockmodeling of relatively sparse binary networks (where we also expect sparse non-null blocks) is problematic. The use of regular equivalence often results in almost all units being classified in the same equivalence class, while using structural equivalence (binary version) only finds very small complete blocks. Two possible ways of blockmodeling such networks within a binary generalized blockmodeling approach are presented. It is also shown that sum of squares (homogeneity) generalized blockmodeling according to structural equivalence is appropriate for this task, although it suffers from "the null block problem". A solution to this problem is suggested that makes the approach even more suitable. All approaches are also applied to an empirical example. My general suggestion is to use either binary blockmodeling according to structural equivalence with different weights for inconsistencies or sum of squares (homogeneity) blockmodeling with null and constrained complete blocks. The second approach is more appropriate when we want complete blocks to have rows and columns of similar densities and differentiate among complete blocks based on densities. If these aspects are not important the first approach is more appropriate as it does in general produce "cleaner" null blocks.