Argumentation is used by people both internally, by evaluating arguments and counterarguments to make sense of a situation and take a decision, and externally, e.g., in a debate, by exchanging arguments to reach an agreement or to promote an individual position. In this context, the assessment of the quality of the arguments is of extreme importance, as it strongly influences the evaluation of the overall argumentation, impacting on the decision making process. The automatic assessment of the quality of natural language arguments is recently attracting interest in the Argument Mining field. However, the issue of automatically assessing the quality of an argumentation largely remains a challenging unsolved task. Our contribution is twofold: first, we present a novel resource of 402 student persuasive essays, where three main quality dimensions (i.e., cogency, rhetoric, and reasonableness) have been annotated, leading to 1908 arguments tagged with quality facets; second, we address this novel task of argumentation quality assessment proposing a novel neural architecture based on graph embeddings, that combines both the textual features of the natural language arguments and the overall argument graph, i.e., considering also the support and attack relations holding among the arguments. Results on the persuasive essays dataset outperform state-of-the-art and standard baselines’ performance.