  We note that building a magnetic Laplacian from the Markov transition matrix,
rather than the graph adjacency matrix, yields several benefits for the
magnetic eigenmaps algorithm. The two largest benefits are that the embedding
becomes more stable as a function of the rotation parameter g, and the
principal eigenvector of the magnetic Laplacian now converges to the page rank
of the network as a function of diffusion time. We show empirically that this
normalization improves the phase and real/imaginary embeddings of the
low-frequency eigenvectors of the magnetic Laplacian.
