  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.
