As a software system is a complex artifact, the interaction between classes exerts a potential impact on software quality, with the cascading propagation effect of software defects as a typical case. How to accurately predict the reasonable relationship between classes in the software system and optimize the design structure is still an open problem in software quality assurance. From the perspective of software network, this study comprehensively considers the interactions between classes in a software system (class external graph, CEG), and those between internal methods of each class (class internal graph, CIG). The software system is abstracted into a software network with a graph of graphs structure. As a result, a class interaction prediction method based on the graph of graphs convolutional network is proposed. Firstly, the initial characteristics of class nodes are obtained through the convolution of each CIG. Then the representation vector of class nodes is updated through the convolution of CEG, and finally, the evaluation values between class nodes are calculated for interaction prediction. The experimental results on six Java open source projects show that the graph of graphs structure is helpful to improve the representation of software system structure. The average growth rates of the area under the curve (AUC) and average precision (AP) of the proposed method are more than 5.5% compared with those of the conventional network embedding methods. In addition, the average growth rates of AUC and AP are more than 9.36% and 5.22%, respectively compared with those of the two peer methods.