nigsp.operations.laplacian.symmetric_normalised_laplacian

nigsp.operations.laplacian.symmetric_normalised_laplacian(mtx, d=None, fix_zeros=True)

Compute symmetric normalised Laplacian (SNL) matrix.

The SNL is obtained by pre- and post- multiplying mtx by the square root of the inverse of the diagonal and subtract the result from the identity matrix. Alternatively, it is possible to specify a different diagonal to do so. With zero-order nodes, the diagonals will contain 0s, returning a Laplacian with NaN elements. To avoid that, 0 elements in d will be changed to 1.

Parameters:

mtxnumpy.ndarray

A [structural] matrix

dnp.ndarray or None, optional

Either an array or a diagonal matrix. If specified, d will be used as the normalisation factor (not the degree matrix).

fix_zerosbool, optional

Whether to change 0 elements in the degree matrix to 1 to avoid multiplying by 0

Returns:

numpy.ndarray

The symmetric normalised laplacian of mtx

Raises:

ValueError

If d in not a diagonal matrix or an array If d and mtx have different shapes.

Notes

This is here mainly for tests and legacy code, but it would be better not to use it!

https://en.wikipedia.org/wiki/Laplacian_matrix#Symmetrically_normalized_Laplacian_2