Relating the mean first passage times for continuous and discrete time random walks on complex networks

Abstract

We study random walks on complex networks and present a continuous time generalization that considers uncorrelated waiting times which have a finite mean waiting time, and this leads to a Poisson number density of steps. We then show that the mean first passage time (MFPT) between two nodes in continuous time is related linearly by the mean waiting time to the to the MFPT in the discrete case, which has an exact expression. Thus, the random walk centrality, which reveals relative differences in the MFPT, may determine aspects of the dynamics of transport processes on networks for both the discrete and continuous time cases.