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Due to the severe damage and huge loss caused by natural disasters to road networks, the protection of the road network is essential. Edge importance identification can help preserve the road network by protecting key edges. This paper proposes a new network performance measure method and introduces a new edge load redistribution method in cascading failure model. To identify different edge importance in the network, this paper proposes three edge importance evaluation metrics, including information entropy of degree values, information entropy of iterative factors and two-dimensional evaluation metric based on the Pareto non-dominated set which combines two single metrics. A case study of highway road in Sichuan province with 204 nodes and 322 edges which was affected by Luding Earthquake is conducted to demonstrate the best one of the three metrics, including data from the Department of Transport of Sichuan Province. The final results of the chi-square test and Kendall’s correlation coefficient comparing the importance ranking of the three metrics with the ranking derived from the network performance assessment model indicate that the two-dimensional evaluation metrics have the best performance and that the road network tends to collapse at the same time when attacked against the road network under different edge rankings, suggesting that the effect of cascading failures should be limited early.