Comparing different methods for one-mode homogeneity blockmodeling according to structural equivalence on binary networks

One-mode homogeneity blockmodeling is an approach to clustering networks that searches for partitions of units in a network so that the resulting blocks are as homogeneous as possible. Block is a part of the network that contain (possible) ties from the units of one cluster to the units of another cluster (or ties within a cluster). Typically, sum of squared deviations from the mean is taken as the measure of variability (non-homogeneity). The paper presents the results of a simulation study that applied several methods for this problem to binary networks generated according to structural equivalence. Several versions of homogeneity generalized blockmodeling (using a relocation algorithm), a k-means-based algorithm, and an indirect approach are compared. Since all of the methods being compared try to optimize the same criterion function, this and the Adjusted Rand Index are the main criteria for the comparison. All methods (except the indirect approach, which is not iterative) were given the same amount of time to find the best possible solution. The overall conclusion is that the k-means approach is advised in most cases, except when smaller networks (200 units) are being partitioned into larger number of clusters, in which case the homogeneity generalized blockmodeling is preferred.