I’ve been looking at the original PageRank paper and upon careful reading, I’ve identified that there may be a subtle bug in the original PageRank paper. I don’t think it particularly matters or perhaps I’m crazy, but on Page 4 it says the rank vector R = cAR, but that is inaccurate; that would make your rank a sum of the rank outflows, given the definition of A_uv!

The right way to write this is R = cRA.