Open-source licenses can promote the development of machine learning by allowing others to access, modify, and redistribute the training dataset. However, not all open-source licenses may be appropriate for data sharing, as some may not provide adequate protections for sensitive or personal information such as social network data. Additionally, some data may be subject to legal or regulatory restrictions that limit its sharing, regardless of the licensing model used. Hence, obtaining large amounts of labeled data can be difficult, time-consuming, or expensive in many real-world scenarios. Few-shot graph classification, as one application of meta-learning in supervised graph learning, aims to classify unseen graph types by only using a small amount of labeled data. However, the current graph neural network methods lack full usage of graph structures on molecular graphs and social network datasets. Since structural features are known to correlate with molecular properties in chemistry, structure information tends to be ignored with sufficient property information provided. Nevertheless, the common binary classification task of chemical compounds is unsuitable in the few-shot setting requiring novel labels. Hence, this paper focuses on the graph classification tasks of a social network, whose complex topology has an uncertain relationship with its nodes’ attributes. With two multi-class graph datasets with large node-attribute dimensions constructed to facilitate the research, we propose a novel learning framework that integrates both meta-learning and contrastive learning to enhance the utilization of graph topological information. Extensive experiments demonstrate the competitive performance of our framework respective to other state-of-the-art methods.