The problem of re-identify persons across single disjoint camera-pairs has received great attention from the community. Despite this, when the re-identification process has to be carried out on a wide camera network additional problems arise and deny the direct application of existing solutions. Thus, a different approach has to be considered. In particular, existing approaches have neglected the importance of the network topology (i.e., the configuration of the monitored area) in such a process. To try filling such a gap, we propose a distributed person re-identification framework which brings in the following contributions: (i) a weighted camera matching cost that measures the re-identification performance between cameras in the network; (ii) a derivation of the distance vector algorithm that yields to network topology learning and allows us to prioritize and limit the cameras inquired for the re-identification; (iii) a network consensus weighted rank fusion solution that allows us to perform the re-identification in a robust fashion. Results on four benchmark datasets show that the proposed approach brings to significant network-wise re-identification improvements.