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We adopt the statistical framework on robustness proposed by Watson and Holmes in 2016 and then tackle the practical challenges that hinder its applicability to network models. The goal is to evaluate how the quality of an inference for a network feature degrades when the assumed model is misspecified. Decision theory methods aimed to identify model missespecification are applied in the context of network data with the goal of investigating the stability of optimal actions to perturbations to the assumed model. Here the modified versions of the model are contained within a well defined neighborhood of model space. Our main challenge is to combine stochastic optimization and graph limits tools to explore the model space. As a result, a method for robustness on exchangeable random networks is developed. Our approach is inspired by recent developments in the context of robustness and recent works in the robust control, macroeconomics and financial mathematics literature and more specifically and is based on the concept of graphon approximation through its empirical graphon.