Interbrain Networks Geometry

---
name: interbrain-networks-geometry
description: "Geometric framework for analyzing inter-brain networks in social neuroscience. Uses discrete geometry and curvature distributions to identify critical transitions in neural connectivity during social interactions, moving beyond correlation-based synchrony metrics. Activation: inter-brain networks, hyperscanning, social neuroscience, discrete geometry, curvature, network topology, synchrony, social interaction, EEG, fNIRS"
metadata:
  arxiv_id: "2509.10650"
  published: "2025-09-12"
  authors: "Nicolás Hinrichs, Noah Guzmán, Melanie Weber"
  tags: [inter-brain-networks, discrete-geometry, hyperscanning, social-neuroscience, curvature, network-topology]
---

# Interbrain Networks Geometry

## Overview

Geometric framework for analyzing inter-brain connectivity during social interactions using discrete geometry and curvature distributions, replacing traditional correlation-based synchrony metrics.

## Core Innovation

### Beyond Correlation-Based Synchrony
Traditional inter-brain synchrony analysis relies on fixed correlation metrics that only provide descriptive observations. This framework introduces geometric insights to capture dynamic reconfigurations in neural interactions.

### Discrete Geometry Approach
- Models inter-brain networks as discrete geometric structures
- Tracks evolving topology during social exchanges
- Identifies critical transitions using entropy metrics from curvature distributions

## Methodology

### Pipeline
1. **Network Construction**: Build inter-brain connectivity graphs from hyperscanning data (EEG/fNIRS)
2. **Geometric Embedding**: Map networks to discrete geometric space
3. **Curvature Analysis**: Compute curvature distributions across network nodes
4. **Entropy Computation**: Calculate entropy metrics from curvature distributions
5. **Transition Detection**: Identify critical connectivity changes via entropy peaks

### Key Metrics
- **Curvature Distribution**: Quantifies local network geometry
- **Geometric Entropy**: Measures topological complexity
- **Transition Points**: Entropy maxima indicate critical reconfigurations

## Applications

- Hyperscanning studies (dyadic interactions, group dynamics)
- Social cognition research (theory of mind, empathy, cooperation)
- Clinical applications (autism, social anxiety, schizophrenia)
- Human-AI interaction studies

## Advantages Over Traditional Methods

- Captures dynamic reconfigurations, not just static correlations
- Provides mechanistic insights into network topology changes
- Identifies critical transition points in social processing
- Compatible with multiple imaging modalities (EEG, fNIRS, fMRI)

## Biological Interpretation

Geometric transitions may reflect:
- Shifts in social cognitive strategies
- Alignment of mental models between interactants
- Emergence of shared representations
- Breakdown/recovery of social rapport

## Pitfalls

- Requires sufficient temporal resolution to capture transitions
- Geometric embedding choices affect curvature computations
- Entropy metrics sensitive to network density and thresholding
- Interpretation of geometric features requires domain expertise

## Related Concepts

- Hyperscanning
- Inter-brain synchrony
- Social neuroscience
- Network topology
- Discrete differential geometry
- Critical transitions in complex systems