The minimum scale backbone network frame of power optical cable network contains important communication and hub stations, bridge links and other key entities, and meets the requirements of connectivity constraints. To mine the backbone network of the power optical cable network, a network mining algorithm based on minimum critical dominating structure is proposed. First, according to the physical topology of a provincial power optical cable network, a representative model of the power optical cable network is constructed. Second, to identify the critical edge of network, a measurement method of critical edge is proposed based on the minimum critical dominating structure. Finally, an algorithm based on the minimum critical dominating structure is designed to realize the mining of the backbone network. Two groups of experiments are designed using the provincial and the southern power optical cable networks in Jilin Province. The algorithm and two classical methods are used to mine the backbone network. Based on this, a deliberate attack is simulated on the power optical cable network, and the change trend of network connectivity is compared and analyzed to verify the effectiveness of the algorithm. This work is supported by the Sci & Tech Research Project of Jilin Education Department (No. JJKH 20220111KJ).