Power method is not matrix-matrix multiplication (which is not N^3, BTW [1]), but rather matrix-vector multiplication. So the power method is N^2*k where k is the number of iterations required to reach precision (usually polylogarithmic).
All this being said, scalability is _obviously_ a non-issue when talking about a matrix of programming languages. All methods are constant time.
Oh right, of course, because you're iterating the distribution. Duh.
And yea, mat mul is not N^3 theoretically, but most implementations are. I've heard that some (mkl maybe) are 2.8, but haven't had someone point code to me. My personal attempts at implementing Strassen were slower than a tuned N^3 implementation, at least for matrices that fit into memory.
It's actually the second highest eigenvalue. The highest eigenvalue is always 1 for stochastic matrices.