graph shift operator

We can define more general diffusion processes by defining the matrix $S\in {\mathbb{R}}^{n\times n}$ such that

(can only equal 0 along the diagonal?)

This matrix is called the graph shift operator (GSO). We way $z=Sx$ is a (graph) "shift" or diffusion of $x$ by $S$.

The most common operators are the adjacency matrix and the graph laplacian

Note that we can always recover the local implementations:

• adjacency matrix
• degree matrix
• graph laplacian
• random walk matrix
• random walk laplacian
• normalized adjacency matrix
• normalized graph laplacian