Fig. 5. Schematic of geometric structural connectivity null algorithm.

a The brain overlay shows the position of all electrodes from a sample patient (#5). Selected electrodes are colored-coded (dark red). b We create geometric null by resampling the patient’s brain regions. At the first step, we find two random distant brain regions and find a pair of empirically sampled brain regions such that the Euclidean distance between the empirical pair maximally matches that of the resampled null pair. The red circles in panel a highlight the empirically sampled electrodes and the center of corresponding null regions with red spheres. Next, out of all possible remaining 598 null regions of interest and the remaining N − 2 (N = total number of selected electrodes) empirically sampled regions, we find two brain regions, one from null and one empirical, with the most similar distances to the regions identified at the first step. At each following step, we repeat this process until we resample N null regions. Here we illustrate this procedure by showing an example of matched empirical (color-coded circles in panel a) and null (color-coded spheres in panel b) regions over five steps.