This project assesses the importance of bank-degree statistics on the probability of default ofbanks in the financial system. A network of banks linked by obligations is generated and studiedunder contagion. If the system faces heterogeneity in the amount of defaults, bank-specificinformation is valuable to measure the risk of contagion in the network. In contrast, when themajority of the system is in a single state (default, survive) degree statistics do not add valuableinformation. In a crisis, regulators can use the information of degree statistics to prevent wavesof contagion and enhance the resilience of the system.