🤖 AI Summary
This paper addresses the challenge of quantifying polarization in social networks by proposing a novel “dimensional decay” paradigm, formally defining polarization as the systematic loss of independent dimensions in graph embedding space. Methodologically, it leverages random dot-product graph embeddings combined with singular value decomposition (SVD) to directly characterize polarization dynamics via rank decay—bypassing traditional indirect metrics based on distance or modularity. Using stochastic block model (SBM) simulations and empirical analysis—including Twitter discussions on climate policy in New Zealand and global COP discourse—the study demonstrates a statistically significant positive correlation between declining embedding dimensionality and increasing polarization. SBM experiments further reveal that both heightened community segregation and increased influence of dominant nodes lead to pronounced dimensional decay. This framework provides an interpretable, computationally tractable, geometric perspective for modeling polarization.
📝 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.