Graph Laplacian Spectrum of Structural Brain Networks is Subject-Specific, Repeatable but Highly Dependent on Graph Construction Scheme

Abstract

AbstractThe human brain is a complex network that can be summarized as a graph where nodes refer to anatomical brain regions while edges encode the neuronal interactions or structural connections between them at both the micro and macroscopic levels, allowing the application of graph theory to investigate the network brain architecture. Various network metrics have been proposed and adopted so far describing both local and global properties of the relevant brain network. It has been proposed that connectomic harmonic patterns that emerged from the brain’s structural network underlie the human brain’s resting-state activity. Connectome harmonics refer to Laplacian eigenfunctions of the structural connectivity matrices (2D) and is an extension of the well-known Fourier basis of a signal (1D). The estimation of the normalized graph Laplacian over a brain network’s spectral decomposition can reveal the connectome harmonics (eigenvectors) corresponding to certain frequencies (eigenvalues). Here, we used test-retest dMRI data from the Human Connectome Project to explore the repeatability of connectome harmonics and eigenvalues across five graph construction schemes. Normalized Laplacian eigenvalues were found to be subject-specific and repeatable across the five graph construction schemes, but their range is highly dependent on the graph construction scheme. The repeatability of connectome harmonics is lower than that of the Laplacian eigenvalues and shows a heavy dependency on the graph construction scheme. In parallel, we investigated the properties of the structural networks and their relationship with the Laplacian spectrum. Our results provide a proof of concept for repeatable identification of the graph Laplacian spectrum of structural brain networks based on the selected graph construction scheme.