Asymptotic analysis of first passage time in complex networks

Abstract

The first passage time (FPT) distribution for random walks in complex networks is calculated through an asymptotic analysis. For a network with size N and short relaxation time τ≪N, the computed mean first passage time (MFPT), which is the inverse of the decay rate of FPT distribution, is inversely proportional to the degree of the destination. These results are verified numerically for the paradigmatic networks with excellent agreement. We show that the range of validity of the analytical results covers networks that have short relaxation time and high mean degree, which turn out to be valid to many real networks.