Mobile video communication and Internet of Things are playing a more and more important role in our daily life. Mobile Edge Computing (MEC), as the essential network architecture for the Internet, can significantly improve the quality of video streaming applications. The mobile devices transferring video flow are often exposed to hostile environment, where they would be damaged by different attackers. Accordingly, Mobile Edge Computing Network is often vulnerable under disruptions, against either natural disasters or human intentional attacks. Therefore, research on secure hub location in MEC, which could obviously enhance the robustness of the network, is highly invaluable. At present, most of the attacks encountered by edge nodes in MEC in the IoT are random attacks or random failures. According to network science, scale-free networks are more robust than the other types of network under the random failures. In this paper, an optimization algorithm is proposed to reorganize the structure of the network according to the amount of information transmitted between edge nodes. BA networks are more robust under random attacks, while WS networks behave better under human intentional attacks. Therefore, we change the structure of the network accordingly, when the attack type is different. Besides, in the MEC networks for mobile video communication, the capacity of each device and the size of the video data influence the structure significantly. The algorithm sufficiently takes the capability of edge nodes and the amount of the information between them into consideration. In robustness test, we set the number of network nodes to be 200 and 500 and increase the attack scale from 0% to 100% to observe the behaviours of the size of the giant component and the robustness calculated for each attack method. Evaluation results show that the proposed algorithm can significantly improve the robustness of the MEC networks and has good potential to be applied in real-world MEC systems.