The study in mobile ad-hoc networks (MANET) is facing challenges brought by recent discovery of non-exponential behavior of the inter-contact time distribution of mobile nodes. In this paper, we analyze various characteristics of the relative mobility of a random pair of nodes in MANET to show that they produce inter-contact time with different aging properties. First, by fixing one node and resorting to the random walks on directed graphs, we mathematically prove that under four classes of stochastic mobility patterns, the resulting inter-contact times have constant/decreasing/increasing failure rate and new-better-thanused property. Then, we consider the case when both nodes are mobile and use simulation results to uncover the aging property of their inter-contact times under random waypoint models and random walk mobility models. This aging property tells us how to correctly relate the past experience of mobile nodes with their future behavior, thereby allowing tremendous opportuni...