Generalised blockmodelling of social and relational networks using evolutionary computing

Abstract

Blockmodels have been studied for many years in social network analysis. In blockmodelling, the goal is to uncover a network into its underlying, latent structure. It does so by reducing a graph into a set of roles, where each role is a set of vertices having similar interactions with other roles. For example, we could decompose an airport routing network into a core-periphery structure of hub and spokes airports. Much prior work has studied how to use probabilistic graphical models to find blockmodels, but there has been little work in allowing users’ supervision and feedback into the fitting and modelling process. Generalised blockmodelling allows users to pre-specify role-to-role interaction patterns and other constraints, which allows users to test models and relationship hypotheses and directly incorporate known biases and constraints. In addition, generalised blockmodelling allows multiple definitions of relational equivalences to co-exist simultaneously in a single model, permitting more general models. The existing approaches to fit generalised blockmodels are not scalable beyond networks of 100 vertices. In this article, we present two new algorithms, a genetic algorithm-based and a simulated annealing based approach, that are multiple times faster than existing approaches. We also demonstrate the usefulness of generalised blockmodelling by fitting to several medium-sized real world networks that previous methods were not able to analyse, and evaluate the efficiency and accuracy on synthetic datasets.