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On a Geometry of Interbrain Networks

Nicolás Hinrichs, Noah Guzmán, Melanie Weber

TL;DR

The paper seeks to move beyond descriptive interbrain synchrony by introducing a discrete-geometry framework for time-varying interbrain networks in hyperscanning. It introduces Forman-Ricci and Ollivier-Ricci curvature as tools to characterize network reconfigurations and information flow, using the entropy of curvature distributions to detect phase transitions. Through toy-model simulations and theoretical connections to information routing, the approach offers mechanistic insights into how social brains coordinate. The framework is intended to be applicable across EEG, fNIRS, and fMRI hyperscanning, enabling richer cross-modality interpretations of social neural dynamics.

Abstract

Effective analysis in neuroscience benefits significantly from robust conceptual frameworks. Traditional metrics of interbrain synchrony in social neuroscience typically depend on fixed, correlation-based approaches, restricting their explanatory capacity to descriptive observations. Inspired by the successful integration of geometric insights in network science, we propose leveraging discrete geometry to examine the dynamic reconfigurations in neural interactions during social exchanges. Unlike conventional synchrony approaches, our method interprets inter-brain connectivity changes through the evolving geometric structures of neural networks. This geometric framework is realized through a pipeline that identifies critical transitions in network connectivity using entropy metrics derived from curvature distributions. By doing so, we significantly enhance the capacity of hyperscanning methodologies to uncover underlying neural mechanisms in interactive social behavior.

On a Geometry of Interbrain Networks

TL;DR

The paper seeks to move beyond descriptive interbrain synchrony by introducing a discrete-geometry framework for time-varying interbrain networks in hyperscanning. It introduces Forman-Ricci and Ollivier-Ricci curvature as tools to characterize network reconfigurations and information flow, using the entropy of curvature distributions to detect phase transitions. Through toy-model simulations and theoretical connections to information routing, the approach offers mechanistic insights into how social brains coordinate. The framework is intended to be applicable across EEG, fNIRS, and fMRI hyperscanning, enabling richer cross-modality interpretations of social neural dynamics.

Abstract

Effective analysis in neuroscience benefits significantly from robust conceptual frameworks. Traditional metrics of interbrain synchrony in social neuroscience typically depend on fixed, correlation-based approaches, restricting their explanatory capacity to descriptive observations. Inspired by the successful integration of geometric insights in network science, we propose leveraging discrete geometry to examine the dynamic reconfigurations in neural interactions during social exchanges. Unlike conventional synchrony approaches, our method interprets inter-brain connectivity changes through the evolving geometric structures of neural networks. This geometric framework is realized through a pipeline that identifies critical transitions in network connectivity using entropy metrics derived from curvature distributions. By doing so, we significantly enhance the capacity of hyperscanning methodologies to uncover underlying neural mechanisms in interactive social behavior.

Paper Structure

This paper contains 9 sections, 4 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. A Graph Geometry Toolkit
  3. The Case of Hyperscanning
  4. Interbrain Networks and their Synchrony
  5. Capturing Phase Transitions
  6. Capturing Information Routing Strategies
  7. Towards an Interbrain Geometry
  8. Ollivier's Ricci curvature
  9. Hyperscanning modalities across conditions

Figures (1)

  • Figure 1: Simulations of time-varying brain networks modeled as weighted small-world networks with varying rewiring probability. A–D: Four examples with $N=100$, mean degree $K=5$, and different $p$, generated using Muldoon2016-mg. E: Entropy of the FRC distribution as $p$ evolves from 0 to 1 for $N=1000$, $K=50$ (note phase transition around $p=10^{-2}$). F: Corresponding quantiles of the FRC distribution. Solid curves show the median over 200 replications; shaded areas mark 0.05 and 0.95 quantiles.