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We model a stylized banking system where banks are characterized by the amount of capital, cash reserves and their exposure to the interbank loan market as borrowers as well as lenders. A network of interbank lending is established that is used as a transmission mechanism for the failure of banks through the system. We trigger a potential banking crisis by exogenously failing a bank and investigate the spread of this failure within the banking system. We find the obvious result that the size of the bank initially failing is the dominant factor whether contagion occurs, but for the extent of its spread the characteristics of the network of interbank loans are most important. These results have implications for the regulation of banking systems that are briefly discussed, most notably that a reliance on balance sheet regulations is not sufficient but must be supplemented by considerations for the structure of financial linkages between banks.