Hodge-Decomposition of Functional Brain Networks

We propose to analyze dynamically changing brain networks by decomposing them into three orthogonal components through the Hodge decomposition. We propose to quantify the magnitude and relative strength of each component. We performed extensive simulation studies with known ground truth. The Hodge decomposition is then applied to the dynamically changing human brain networks obtained from a resting-state functional magnetic resonance imaging study. Our results indicate that the components of the Hodge decomposition contain biologically interpretable topological features that provide statistically significant findings not easily captured by traditional methods.