This work examines the problem of topology inference over discrete-time nonlinear stochastic networked dynamical systems. The goal is to recover the underlying digraph linking the network agents, from observations of their state-evolution. The dynamical law governing the state-evolution of the interacting agents might be nonlinear, i.e., the next state of an agent can depend nonlinearly on its current state and on the states of its immediate neighbors. We establish sufficient conditions that allow consistent graph learning over a special class of networked systems, namely, logistic-type dynamical systems.