Fig. 4

The comparison of the nodal path length (x axis) for the 620-ROI structural connectome versus their distances to the center in various spaces. The correlation coefficients for each subplot is r ² = 0.144 (anatomic space), r ² = 0.427 (MDS), and r ² = 0.828 (Isomap). As expected, a node’s nodal path length does not relate to its distance to the brain’s anatomic center (left subplot), but overall, mostly linearly maps onto its Euclidean distance to the embedding’s topological center when a nonlinear technique such as Isomap is used. Indeed, as the dimensionality-reduction technique becomes more advanced (from no dimensionality reduction to linear reduction to nonlinear reduction), better representations of the intrinsic geometry are achieved and embedded in a 3D Euclidean space