Hodge Decomposition of Functional Human 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 components. We performed extensive simulation studies with the known ground truth. The Hodge decomposition is then applied to the dynamically changing human brain networks obtained from the resting state functional magnetic resonance imaging study. Our study indicates that the components of the Hodge decomposition contain biologically interpretable topological features that provide statistically significant results that are difficult to obtain with the traditional methods.