Skeleton-based action recognition depends on skeleton sequences to detect categories of human actions. In skeleton-based action recognition, the recognition of action scenes with more than one subject is named as interaction recognition. Different from the single-subject action recognition methods, interaction recognition requires an explicit representation of the interaction information between subjects. Recalling the success of skeletal graph representation and graph convolution in modeling the spatial structural information of skeletal data, we consider whether we can embed the inter-subject interaction information into the skeletal graph and use graph convolution for a unified feature representation. In this paper, we propose the interaction information embedding skeleton graph representation (IE-Graph) and use the graph convolution operation to represent the intra-subject spatial structure information and inter-subject interaction information in a uniform manner. Inspired by recent pre-training methods in 2D vision, we propose unsupervised pre-training methods for skeletal data as well as contrast loss. In SBU datasets, JointContrast achieves $98.2\%$ recognition accuracy. in NTU60 datasets, JointContrast respectively achieves $94.1\%$ and $96.8\%$ recognition accuracy under Cross-Subject and Cross-View evaluation metrics.