An algorithm and metric for network decomposition from similarity matrices: Application to positional analysis

We present an algorithm for decomposing a social network into an optimal number of structurally equivalent classes. The k-means method is used to determine the best decomposition of the social network for various numbers of subgroups. The best number of subgroups into which to decompose a network is determined by minimizing the intra-cluster variance of similarity subject to the constraint that the improvement in going to more subgroups is better than a random network would achieve. We also describe a decomposability metric that assesses how closely the derived decomposition approaches an ideal network having only structurally equivalent classes.     

A new criterion function for exploratory blockmodeling for structural and regular equivalence

We present a new criterion function for blockmodeling two-way two-mode relation matrices when the number of blocks as well as the equivalence relation are unknown. For this, we specify a measure of fit based on data compression theory, which allows for the comparison of blockmodels of different sizes and block types from different equivalence relations. We arm an alternating optimization algorithm with this criterion and demonstrate that the method reproduces consensual blockings of three datasets without any pre-specification. We perform a simulation study where we compare our compression-based criterion to the commonly used criterion that measures the number of inconsistencies with an ideal blockmodel.