Fig. 4: Covariance distance in TD and EOS.

A Correlations between geodesic distances and covariance gradients and covariance matrices. The node-wise geodesic distance degree was calculated by averaging the geodesic distance for each node. The spin test was used to control for spatial autocorrelations (p_spin < 0.05, 10,000 times)⁶⁵. The edge-wise geodesic distance was then correlated with the structural covariance matrix, and the statistical significance was assessed using permutation tests (p_perm < 0.05, 10,000 times). B Covariance distance calculation. For each group, we column-wise thresholded the structural covariance matrix at 90%, and then binarized it as a mask. Covariance distance was then calculated using the averaging geodesic distance profiles of a seed region multiplied by the mask. C Effects of disease on covariance distances. In the left line graph, one dot represents a bin along the normative gradient axis, showing t values evaluated by paired t-tests (* represents q_FDR < 0.05). In the right box-and-whisker plots, the red horizontal lines in the box indicate the mean of each group, and the lower and upper horizontal lines indicate the lower and upper quartiles, respectively. Green boxes represent covariance distances of EOS patients and gray boxes represent TD controls.