Polarization identification on multiple timescale using representation learning on temporal graphs in Eulerian description

Social media is often described as both reflecting and distorting real-life debates. Indeed, social division occurs not only offline but also online on various political topics or scientific controversies. Several studies propose tools to identify and quantify online controversies through stance detection or polarization measures. While polarization is typically studied as a "snapshot" in time of a social network, we consider it as a temporal process. Moreover, the recent evolution in temporal graph representation learning provides new tools to directly combine time, content and graph topology. Current techniques that characterize polarization are beginning to use these tools, typically using a Lagrangian description which focuses on user trajectories. In this article, we make a case for approaching these problems with a Eulerian description, the concurrent description in fluid mechanics. In this description, the temporal evolution of nodes embeddings is represented with a deformation of velocity vector fields. Finally, we validate our method on a retweet graph from the last French presidential election campaign.