For intermittently connected mobile networks such as sparsely-deployed vehicular networks, it is of great interest to characterize the distribution of encounter times. We consider a very general mobility model in which each device is assumed to be moving through a given graph following a general random walk with arbitrary transition probabilities. We consider first the pairwise inter-encounter time distribution for a pair of random walkers and present a recursive polynomial-time computation that yields the exact solution. We then consider the individual-to-any inter-encounter time (i.e., the time between contacts of a particular walker with any of the other walkers in the population). For this harder problem, we give an approximate computation that is also polynomial time. We validate the accuracy of the presented solutions using numerical simulations. We discuss how the model can be generalized to consider multiple populations.