# A mathematical perspective on edge-centric brain functional connectivity

arXiv: https://arxiv.org/abs/2106.10631 · HTML: https://mlsanity.com/paper/2106.10631/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2021.

## Built on by (most cited first, 2 of 2)

- [Rethinking Functional Brain Connectome Analysis: Do Graph Deep Learning Models Help](https://mlsanity.com/paper/2501.17207/) (2025)
- [Extracting the Multiscale Causal Backbone of Brain Dynamics](https://mlsanity.com/paper/2311.00118/) (2023)

## Abstract (arXiv)

Edge time series are increasingly used in brain functional imaging to study the node functional connectivity (nFC) dynamics at the finest temporal resolution while avoiding sliding windows. Here, we lay the mathematical foundations for the edge-centric analysis of neuroimaging time series, explaining why a few high-amplitude cofluctuations drive the nFC across datasets. Our exposition also constitutes a critique of the existing edge-centric studies, showing that their main findings can be derived from the nFC under a static null hypothesis that disregards temporal correlations. Testing the analytic predictions on functional MRI data from the Human Connectome Project confirms that the nFC can explain most variation in the edge FC matrix, the edge communities, the large cofluctuations, and the corresponding spatial patterns. We encourage the use of dynamic measures in future research, which exploit the temporal structure of the edge time series and cannot be replicated by static null models.