Network inhibition is a denial-of-service attack where the adversary attempts to disconnect network elements by disabling a limited number of communication links or nodes. We analyze a common variation of network inhibition where the links have infinite capacity and the goal of the attacker is to deny connections from a single server to as many clients as possible. The problem is defined formally and shown to be NP complete. Nevertheless, we develop a practical technique for network-inhibition analysis based on logic programming with stable-model semantics. The analysis scales well up to moderate-size networks. The results are a step towards quantitative analysis of denial of service and they can be applied to the design of robust network topologies.