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For assessing the security and optimal strengthening of large enterprise networks, this paper proposes a new approach uses configuration information on firewalls and vulnerability information on all network devices to build defense graphs that show the attack and defense strategy. Some models including a defense graph model, attack-defense taxonomy and cost quantitative model, and Attack-Defense Game (ADG) model. We regard the interactions between an attacker and the defender as a two-player, non-cooperative, zero-sum, finite strategic game and formulate the ADG model for the game. An algorithm for optimal strengthening strategy selection based on those models is proposed. Optimal strengthening strategies with minimizing costs are used to defend the attack and strengthening the network in advance. And finally, we perform empirical experiments to verify the effectiveness of the model experiment results indicate that our models and methods are effective and efficient.