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This paper presents a graph-based approach to network vulnerability analysis. The method is flexible, allowing analysis of attacks from both outside and inside the network. It can analyze risks to a specific network asset, or examine the universe of possible consequences following a successful attack. The graph-based tool can identify the set of attack paths that have a high probability of success (or a low "effort" cost) for the attacker. The system could be used to test the effectiveness of making configuration changes, implementing an intrusion detection system, etc.
Phillips et al. (1998) studied this question.