Natural Language Processing and Machine Learning have considerably advanced Computational Literary Studies. Similarly, the construction of co-occurrence networks of literary characters, and their analysis using methods from social network analysis and network science, have provided insights into the micro- and macro-level structure of literary texts. Combining these perspectives, in this work we study character networks extracted from a text corpus of J.R.R. Tolkien's Legendarium. We show that this perspective helps us to analyse and visualise the narrative style that characterises Tolkien's works. Addressing character classification, embedding and co-occurrence prediction, we further investigate the advantages of state-of-the-art Graph Neural Networks over a popular word embedding method. Our results highlight the large potential of graph learning in Computational Literary Studies.