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

It has been proposed that the estimation of the normalized graph Laplacian over a brain networks spectral decomposition can reveal the connectome harmonics (eigenvectors) corresponding to certain frequencies (eigenvalues). Here, I used test-retest dMRI data from the Human Connectome Project to explore the repeatability, and the influence of graph construction schemes on a) graph Laplacian spectrum, b) topological properties, c) high-order interactions (3,4-motifs,odd-cycles), and d) their associations on structural brain networks (SBN). Additionally, I investigated the performance of subjects identification accuracy (brain fingerprinting) of the graph Laplacian spectrum, the topological properties, and the high-order interactions. Normalized Laplacian eigenvalues were found to be subject-specific and repeatable across the five graph construction schemes. The repeatability of connectome harmonics is lower than that of the Laplacian eigenvalues and shows a heavy dependency on the graph construction scheme. A repeatable relationship between specific topological properties of the SBN with the Laplacian spectrum was also revealed. The identification accuracy of normalized Laplacian eigenvalues was absolute (100%) across the graph construction schemes, while a similar performance was observed for a combination of topological properties of SBN (communities,3,4-motifs, odd-cycles) only for the 9m-OMST. Collectively, Laplacian spectrum, topological properties, and high-order interactions characterized uniquely SBN.