We consider the problem of locating the source of diffusion of a message or of a virus in a large network, from a sparse set of nodes (sensors) that can only indicate the time at which they have received the message. When propagation times are (close to) deterministic values, the smallest number of sensors required to realize the task is the double metric dimension of the graph. We compute tight bounds for this quantity in a number of topologies that include Erdös-Renyi graphs.