What the interpretation of the normalized adjacency matrix raised to a power $K$?
If we take the exponent of an adjacency matrix we get the number of walks, but what about if we do that for the normalized adjacency matrix?
$\mathbf{S} = \mathbf{D}^{-\frac{1}{2}}\tilde{\mathbf{A}}\mathbf{D}^{-\frac{1}{2}}$
$\tilde{A} = (A+I)$ and then raising $\mathbf{S}$ to a power:
$\mathbf{S}^K$
what is the interpretation that can be produced here for the result of $\mathbf{S}^K$?
link to question of power of Laplacian but not for the normalized Laplacian
