Nowadays, the number of people and companies using the Web to search for and advertise job opportunities is growing apace, making data related to the Web labor market a rich source of information for understanding labor market dynamics and trends. In this paper, the emerging term labor market intelligence (LMI) refers to the definition of AI algorithms and frameworks that derive useful knowledge for labor market-related activities, by putting AI into the labor market. At the same time, another branch of AI is developing known as Explainable AI (XAI), whose goal is to obtain interpretable models from current (and future) AI algorithms, given that most of them actually act like black boxes, providing no interpretable explanations of their behavior, as in the case of machine learning. In this paper we connect these two approaches, using a graph model obtained through an NLP-based (Natural Language Processing) methodology for classifying job vacancies. We compare the results obtained with those from a European Project in LMI that employs machine learning for the classification task, to show that our approach is effective and promising.