1. A method comprising the steps of: assigning attack-escalation states of a persistent security threat to respective nodes in a graph, wherein assigning attack-escalation states of the persistent security threat to respective nodes in the graph comprises assigning initial and final attack-escalation states to respective source and target nodes in the graph; assigning defensive costs to respective edges in the graph for preventing transitions between pairs of the nodes, wherein the defensive costs represent costs for preventing respective attack actions; computing a minimum cut of the graph to identify a set of one or more edges that if removed from the graph will prevent the persistent security threat from proceeding from the source node to the target node; and determining a defensive strategy based on the minimum cut; wherein a system comprising information technology infrastructure subject to the persistent security threat is configured in accordance with the defensive strategy in order to deter the persistent security threat; and wherein the steps are performed by a processing device comprising a processor coupled to a memory.