Network reconstruction is an important objective for understanding biological interactions and their role in disease mechanisms and treatment. Yet, even for small systems, contemporary reconstruction methods struggle with critical network properties: (i) edge causality, sign and directionality; (ii) cycles with feedback or feedforward loops including self-regulation; (iii) dynamic network behavior; and (iv) environment-specific effects. Moreover, experimental noise significantly impedes many methods. We report an approach that addresses the aforementioned challenges to robustly and uniquely infer edge weights from sparse perturbation time course data that formally requires only one perturbation per node. We apply this approach to randomized 2 and 3 node systems with varied and complex dynamics as well as to a family of 16 non-linear feedforward loop motif models. In each case, we find that it can robustly reconstruct the networks, even with highly noisy data in some cases. Surprisingly, the results suggest that incomplete perturbation (e.g. 50% knockdown vs. knockout) is often more informative than full perturbation, which may fundamentally change experimental strategies for network reconstruction. Systematic application of this method can enable unambiguous network reconstruction, and therefore better prediction of cellular responses to perturbations such as drugs. The method is general and can be applied to any network inference problem where perturbation time course experiments are possible. ### Competing Interest Statement The authors have declared no competing interest.
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