Abusive behaviors are common on online social networks. The increasing frequency of antisocial behaviors forces the hosts of online platforms to find new solutions to address this problem. Automating the moderation process has thus received a lot of interest in the past few years. Various methods have been proposed, most based on the exchanged content, and one relying on the structure and dynamics of the conversation. It has the advantage of being languageindependent, however it leverages a hand-crafted set of topological measures which are computationally expensive and not necessarily suitable to all situations. In the present paper, we propose to use recent graph embedding approaches to automatically learn representations of conversational graphs depicting message exchanges. We compare two categories: node vs. whole-graph embeddings. We experiment with a total of 8 approaches and apply them to a dataset of online messages. We also study more precisely which aspects of the graph structure are leveraged by each approach. Our study shows that the representation produced by certain embeddings captures the information conveyed by specific topological measures, but misses out other aspects.