A closed time-reversal (TR) cavity has been considered a purely theoretical concept whose experimental realization was assumed to be impossible. In this article, we demonstrate that it is, in fact, possible to realize a closed TR cavity using a network of transmission lines. The network is excited by either lumped voltage or current sources at arbitrary locations, and it is terminated on matched impedances. This system is an exact closed TR cavity in the sense that, in the backward-propagation stage, by back-injecting time-reversed measured responses (voltage or current) generated by a source at each line terminal, a time-reversed copy of the current and voltage distribution in the forward-propagation stage is obtained. We report for the first time an experimental realization of a TR cavity formed by a network of inhomogeneous transmission lines, in which the spatial and temporal signal distribution along the network is reproduced as in a sequence of the system state (i.e., voltages and or current along the lines) being played in reverse. We also discuss the interfering effect of the so-called diverging wave for observation points in the vicinity of the source. An active realization of a TR sink is proposed to effectively overcome the interfering effect caused by the diverging waves.