This paper presents a novel approach to investigate and model the network of euro area banks’ large exposures within the global banking system. Drawing on a unique dataset, the paper documents the degree of interconnectedness and systemic risk of the euro area banking system based on bilateral linkages. We develop a Contagion Mapping model fully calibrated with bank-level data to study the contagion potential of an exogenous shock via credit and funding risks. We find that tipping points shifting the euro area banking system from a less vulnerable state to a highly vulnerable state are a non-linear function of the combination of network structures and bank-specific characteristics.