Measuring changes in polarisation using Singular Value Decomposition of network graphs

Abstract: In this paper we present new methods of measuring polarisation in social networks. We use Random Dot Product Graphs to embed social networks in metric spaces. Singular Value Decomposition of this social network then provider an embedded dimensionality which corresponds to the number of uncorrelated dimensions in the network. A decrease in the optimal dimensionality for the embedding of the network graph means that the dimensions in the network are becoming more correlated, and therefore the network is becoming more polarised. We demonstrate this method by analysing social networks such as communication interactions among New Zealand Twitter users discussing climate change issues and international social media discussions of the COP conferences. In both cases, the decreasing embedded dimensionality indicates that these networks have become more polarised over time. We also use networks generated by stochastic block models to explore how an increase of the isolation between distinct communities, or the increase of the predominance of one community over the other, in the social networks decrease the embedded dimensionality and are therefore identifiable as polarisation processes.