An exact numerical approach to calculate the first passage time for general random walks on a network

We present an exact numerical method to calculate the mean first passage time for the random walk on the network between any source node and any target which contains an arbitrary number of nodes. For the network with the average degree (k) ∼ O(1) and the effective diameter D ∼ ln N or less, the efficiency of our numerical approach is found to exceed all other general numerical methods presented in the literature. Our method can also calculate the average of any function of the first passage time, provided it is finite.