 ![Illustration of the diffusion distance between two red dots as the total number of paths connecting them. The region on the left panel (the Cheeger dumbbell) is "less" connected than the region on the right as there are fewer paths in the former due to the narrow bottleneck in the middle. In particular, the second smallest eigenvalue associated with the Laplace-Beltrami operator (or the Cheeger isoperimetric constant) of the left region is smaller that of the right.[]{data-label="fig:diffussion_dist"}](examples