Detecting Phase Transitions in EEG Hyperscanning Networks Using Geometric Markers

EEG hyperscanning offers valuable insights into neural synchrony during social interactions, yet traditional node-based network metrics may overlook critical topological features. This perspective paper introduces Forman-Ricci curvature, a novel edge-based geometric metric, to characterize time-varying inter-brain coupling networks. Unlike conventional methods, Forman-Ricci curvature provides a quantitative measure of information routing, i.e. capturing how neural network structures expand or contract during dynamic interactions. We outline how this method can be implemented for the analysis of task-specific dual-EEG data; by constructing dynamic networks via a sliding window approach the evolution of network states through changes in curvature distributions is enabled. We propose Forman-Ricci network entropy, a scalar metric derived from the Shannon entropy of curvature distributions, to detect phase transitions in neural dynamics. Additionally, we propose a framework to simulate biophysically realistic dual-brain activity to validate results and optimise algorithm selection for source-space estimation. Our method effectively extends the two-person neuroscience framework by enabling its real-time implementation in multimodal experimental paradigms, offering a novel perspective on information routing within interactive neural systems. By capturing dynamic shifts in inter-brain network states, this approach enables further understanding of the neurobiological process that underlie the reciprocity of social interaction.