The interest in problems related to graph inference has been increasing significantly during the last decade. However, the vast majority of the problems addressed are either static, or systems where changes in one node are immediately reflected in other nodes. In this paper we address the problem of mobility graph estimation, when the available dataset has an asynchronous and time-variant nature. We present a formulation for this problem consisting on an optimization of a cost function having a fitting term to explain the observations with the dynamics of the system, and a sparsity promoting penalty term, in order to select the paths actually used. The formulation is tested on two publicly available real datasets on US aviation and NY taxi traffic, showing the importance of the problem and the applicability of the proposed framework.