Efficient complex systems have a modular structure, but modularity does not guarantee robustness, for efficiency requires also an ingenious interplay of the interacting modular components. The human brain is the elemental paradigm of an efficient robust modular system interconnected as a Network of Networks (NoN). Understanding the emergence of robustness in such modular architectures from the interconnections of its parts is a long-standing challenge which has concerned many scientists. Current models of dependencies in NoN inspired by the power grid express interactions among modules with very breakable couplings which amplify even small shocks, thus preventing functionality. Therefore, we introduce a model of NoN to shape the pattern of brain activations to form a modular environment which is robust. The model predicts the collective influence map of the brain, through the optimization of the influence of the minimal set of core nodes responsible for broadcasting information to the whole NoN. This result may open the way to discover new intervention protocols to control brain activity by targeting influential core nodes prescribed by network theory.