One can observe a dynamic process like an epidemic or a rumor spreading by tracking timestamps when persons become infected or start spreading a rumor. The edges of the underlying network in which this dynamic process unfolds is often hidden. The goal is to recover the edges from such timestamp-information of several dynamic processes. We study the computational complexity of the corresponding optimization problem. Herein, given such observations from multiple dynamic processes, the task is to find a graph with a minimum number of edges that is consistent with all these observations. We differentiate a highly contagious case where each infected person will infect all its neighbors in the graph and a resistant case where a person gets infected only after all its neighbors are infected. While the latter case turns out to be polynomial-time solvable, the former case is NP-complete but efficiently solvable in restricted cases. Our investigations of these two cases reveal connections to the problems of reconstructing the edge set of a graph from vertex covers or from dominating sets, that is, given is set of subsets where each subset forms a vertex cover or each subset forms a dominating set in the (unknown) graph.