For an undirected graph with adjacency matrix $A$, it is straightforward to define the normalized adjacency matrix as
$$ A'=D^{-1/2}AD^{-1/2}$$
where D is the diagonal matrix of degrees of the nodes of the graph.
For a directed graph, however, I'm unclear on how to best define the normalized adjacency matrix. It seems like the most direct extension is to simply consider the diagonal matrix of in- or out-degrees, instead. However, selecting one versus the other would appear to give very different results.
Is there a standard way to define the normalized adjacency matrix for directed graphs?
Best Answer
According to my research, you can normalize directed adjacency graph either by rows or columns.
$A'=D^{−1}A$ or $A'= A D^{−1}$.
Supporting Evidence:
Hope this helps.