Electrical power communication networks undertake complicated power services. They interact with physical power grids all the time, which will result in a high risk to power grids when their electric power communication network is attacked. Therefore, to improve the reliability of power systems, it is of great significance to identify the key links of communication networks. Existing research studies focus more on the risk of power communication services undertaken by communication links, which ignores the frequent interaction between power grids and communications networks. In this paper, from a multi-layer network perspective, an assessment method of communication equipment is proposed in view of the operation characteristics of nodes in different systems as well as the dynamic fault propagation between homogeneous communication nodes. Firstly, we build a model of cyber-physical power interdependent network. Then, for communication nodes, a dynamic model is adopted for cascading failure among the nodes based on the load-capacity model. Afterward, we define an index to evaluate the node importance considering characteristics of the operation of both communication networks and power grids. Finally, a local power grid is taken as an example for verification by comparing the effects of different indexes. The simulation results demonstrate the validity of the evaluation method proposed.