discriminability of a graph filter

The discriminability of a graph filter describes the ability of the filter to tell the difference between different eigenvalues of the shift operator spectrum.

Recall that we can think of the spectrum as a polynomial in the eigenvalues of the shift operator.

The discriminability thus corresponds with $\mid \mid h(\lambda )-h(\lambda +ϵ)\mid \mid$ , or the change in spectral response for a small change in eigenvalue.

If a filter is able to discriminate well between eigenvalues, then it is able to describe which eigenvectors contribute to the task more effectively.