Deep learning plays an important role in the development of artificial intelligence (AI) technology. The security of deep networks has become the crucial thing to be considered. When the deep learning algorithms are implemented in the hardware platform, the interference for topology structure will appear because of cyber-attacks. We analyze the working capacity of acyclic deep networks under the topology attacks and injection attacks. Considering the topology structure of the deep network, the maximum working capacity is studied under the topology attacks and injection attacks. Furthermore, the robustness of the random networks is researched and the structural robustness index (SRI) is proposed to measure the toleration for the topology attacks. This work supplies some suggestions for building a robust deep network and improving the endogenous safety and security (ESS) of the deep networks.