One way to model cascading critical infrastructure failures is through dependency risk graphs. These graphs help assess the expected risk of critical infrastructure dependency chains. This research extends an existing dependency risk analysis methodology towards risk management. The relationship between dependency risk paths and graph centrality measures is explored in order to identify nodes that significantly impact the overall dependency risk. Experimental results using random graphs to simulate common critical infrastructure dependency characteristics are presented. Based on the experimental findings, an algorithm is proposed for efficient risk mitigation. The algorithm can be used to define priorities in selecting nodes for the application of mitigation controls.