  The brain's complex functionality emerges from network interactions that go
beyond dyadic connections, with higher-order interactions significantly
contributing to this complexity. One method of capturing higher-order
interactions is through traversing the brain network using random walks. The
efficacy of these random walks depends on the defined mutual interactions
between two brain entities. More precise capture of higher-order interactions
enables a better reflection of the brain's intrinsic neurophysiological
characteristics. One well-established neurophysiological concept is Homotopic
Functional Connectivity (HoFC), which illustrates the synchronized spontaneous
activity between corresponding regions in the brain's left and right
hemispheres. We employ node2vec, a random walk node embedding approach,
alongside resting-state fMRI from the Human Connectome Project (HCP) to obtain
higher-order feature vectors. We assess the efficacy of different functional
connectivity parameterizations using HoFC. The results indicates that the
quality of capturing higher-order interactions largely depends on the
statistical dependency measure between brain regions. Higher-order interactions
defined by partial correlation, better reflects HoFC compare to other
statistical associations. In this case of first-order interactions, tangent
space embedding more effectively demonstrates HoFC. The findings validate HoFC
and underscore the importance of functional connectivity construction method in
capturing intrinsic characteristics of the human brain.
