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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?

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In this algorithm after computing the transition matrix, we should compute the stationary distribution

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.

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  • $\begingroup$ Thanks a lot for your answer :) .Does this property(I mean the stationary distribution is proportional to left o right eigenvector corresponding to eigenvalue 1 ) true for every type of graph such as directed or undirected,strongly connected or sparse, periodic or aperiodic? $\endgroup$ – Fatime Feb 24 '13 at 5:04

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