Dynamic topology is the essential difference between mobile ad hoc networks and other kinds. It is meaningful in both theory and industry application to study the dynamic topology of mobile ad hoc networks. In this paper, a method is proposed to study the dynamic topology with longest lifetime path. On basis of the previous research, the mathematic model of networks is improved to describe the change of topology. Based on it, the algorithm of longest lifetime path is presented and the distribution of its duration is studied. At the same time, it is proved that the re-routing is minimal with the longest lifetime paths as the routes. Simulation with NS -2 shows that the distribution of lognormal can be used to describe the duration of longest lifetime paths. The results show that the longest lifetime path and minimal re-routing are more suitable than the shortest path as the metrics to measure the dynamic of networks.