Hodge-Laplacian of Brain Networks

TL;DR

This paper introduces a novel method using persistent homology and the Hodge Laplacian to identify and analyze cycles in brain networks, providing new insights into brain function.

Contribution

It presents an efficient algorithm for cycle detection in brain networks and develops statistical inference procedures, validated on simulations and real fMRI data.

Findings

Effective cycle identification in brain networks

Validated methods on simulated and real data

Provides tools for higher-order brain network analysis

Abstract

The closed loops or cycles in a brain network embeds higher order signal transmission paths, which provide fundamental insights into the functioning of the brain. In this work, we propose an efficient algorithm for systematic identification and modeling of cycles using persistent homology and the Hodge Laplacian. Various statistical inference procedures on cycles are developed. We validate the our methods on simulations and apply to brain networks obtained through the resting state functional magnetic resonance imaging. The computer codes for the Hodge Laplacian are given in https://github.com/laplcebeltrami/hodge.