A distributed swarm control strategy based on graph convolutional imitation learning was proposed to deal with the cooperative control of robot swarms under restricted communication conditions. The strategy aimed to improve swarm robustness and enhance the success rate of avoiding swarm splitting based on achieving intra-swarm obstacle avoidance and velocity consistency. A quantitative evaluation index of swarm robustness based on entropy evaluation was proposed to establish the connection between the balanced distribution of node and link importance and cluster robustness. The importance-correlated graph convolutional networks were proposed to realize feature extraction and weighted aggregation of non-Euclidean data under restricted communication conditions. A centralized expert strategy was designed to improve swarm robustness, and the graph convolutional imitation learning method was adopted. Furthermore, a distributed swarm cooperative control strategy was obtained by imitating the centralized expert strategy. Simulation experiments demonstrate that the resulting distributed strategy achieves control effects close to those of the centralized expert strategy based on restricted communication conditions.