  In this paper we address the problem of the calculation of the mean first
passage time (MFPT) on generic graphs. We focus in particular on the mean first
passage time on a node 's' for a random walker starting from a generic,
unknown, node 'x'. We introduce an approximate scheme of calculation which maps
the original process in a Markov process in the space of the so-called rings,
described by a transition matrix of size O(ln N / ln<k> X ln N / ln<k>), where
N is the size of the graph and <k> the average degree in the graph. In this way
one has a drastic reduction of degrees of freedom with respect to the size N of
the transition matrix of the original process, corresponding to an
extremely-low computational cost. We first apply the method to the Erdos-Renyi
random graph for which the method allows for almost perfect agreement with
numerical simulations. Then we extend the approach to the Barabasi-Albert
graph, as an example of scale-free graph, for which one obtains excellent
results. Finally we test the method with two real world graphs, Internet and a
network of the brain, for which we obtain accurate results.
