I want to implement the algorithm of graph partitioning of sparse directed graph. In this algorithm after computing the transition matrix ,we should compute the stationary distribution of the random walk. I don't know how to compute the stationary distribution of random walk in such sparse directed graph.Is there any suggestion?
The stationary distribution is proportional to one of the left or right eigenvectors of the transition matrix, and the corresponding eigenvalue is 1. You can compute this using matlab or other software.