The structure of a complex networked system can be modeled as a graph with nodes representing the agents and the links describing a notion of dynamic coupling between them. Data-driven methods to identify such influence pathways is central to many application domains. However, such dynamically related data-streams originating at different sources are prone to corruption caused by asynchronous time-stamps, packet drops and noise. In this article, we provide a tight characterization of the connectivity structure of the agents that can be constructed based solely on measured data streams that are corrupted. A necessary and sufficient condition that delineates the effects of corruption on a set of nodes is obtained. Here, the generative system that yields the data admits nonlinear dynamic influences between agents and can involve feedback loops. Directed information based concepts are utilized in conjunction with tools from graphical models theory to arrive at the results.