This paper develops a framework for the quantification of operational risk based on a network with functional dependencies that represent work flows for business activities. The functioning of each node depends on stochastic risk factors driven by inputs such as human resources, data and inputs from other nodes. Using analytical and numerical methods, we obtain answers concerning capital allocation, stability, risk figures, the effect of different network structures (called “topological diversification”) and dynamic diversification. Interpreting the results shows that the usual intuition gained from market and credit risk does not apply to the quantification of operational risk.