Source code summaries are short natural language descriptions of code snippets that help developers better understand and maintain source code. There has been a surge of work on automatic code summarization to reduce the burden of writing summaries manually. However, most contemporary approaches mainly leverage the information within the boundary of the method being summarized (i.e., local context), and ignore the broader context that could assist with code summarization. This paper explores two global contexts, namely intra-class and inter-class contexts, and proposes the model CoCoSUM: Contextual Code Summarization with Multi-Relational Graph Neural Networks. CoCoSUM first incorporates class names as the intra-class context to generate the class semantic embeddings. Then, relevant Unified Modeling Language (UML) class diagrams are extracted as inter-class context and are encoded into the class relational embeddings using a novel Multi-Relational Graph Neural Network (MRGNN). Class semantic embeddings and class relational embeddings, together with the outputs from code token encoder and AST encoder, are passed to a decoder armed with a two-level attention mechanism to generate high-quality, context-aware code summaries. We conduct extensive experiments to evaluate our approach and compare it with other automatic code summarization models. The experimental results show that CoCoSUM is effective and outperforms state-of-the-art methods. Our source code and experimental data are available in the supplementary materials and will be made publicly available.