Structural graph descriptors (HKS, diffusion coordinates)

These helpers compute **intrinsic** node descriptors from a within-domain spectral basis (eigenvalues/eigenvectors). They are designed to be reusable across multiple alignment methods (e.g., GRASP, spectral MNN, and as features for UOT costs).

The main entry points are: - [hks_time_grid()] to construct a diffusion-time grid. - [compute_hks_descriptors()] to compute Heat Kernel Signatures (HKS). - [compute_diffusion_coordinates()] to compute diffusion coordinates at one or more times.

Value

See individual functions.

Details

**Basis format**

These functions accept either: - a list with fields `values` (length K) and `vectors` (N x K), or - explicit `values`/`vectors` arguments.

For Laplacian-based bases, the first eigenvalue is typically 0 and corresponds to a constant mode. By default, eigenpairs with `value <= eigen_tol` are dropped.