The traditional way to address the problem of sentiment classification is based on machine learning techniques; however, these models are not able to grasp all the richness of the text that comes from different social media, personal web pages, blogs, etc., ignoring the semantic of the text. Knowledge graphs give a way to extract structured knowledge from images and texts in order to facilitate their semantic analysis. This work proposes a new hybrid approach for Sentiment Analysis based on Knowledge Graphs and Deep Learning techniques to identify the sentiment polarity (positive or negative) in short documents, such as posts on Twitter. In this proposal, tweets are represented as graphs; then, graph similarity metrics and a Deep Learning classification algorithm are applied to produce sentiment predictions. This approach facilitates the traceability and interpretability of the classification results, thanks to the integration of the Local Interpretable Model-agnostic Explanations (LIME) model at the end of the pipeline. LIME allows raising trust in predictive models, since the model is not a black box anymore. Uncovering the black box allows understanding and interpreting how the network could distinguish between sentiment polarities. Each phase of the proposed approach conformed by pre-processing, graph construction, dimensionality reduction, graph similarity, sentiment prediction, and interpretability steps is described. The proposal is compared with character n-gram embeddings-based Deep Learning models to perform Sentiment Analysis. Results show that the proposal is able to outperforms classical n-gram models, with a recall up to 89% and F1-score of 88%.