Representing words into vectors in continuous space can form up a potentially powerful basis to generate high-quality textual features for many text mining and natural language processing tasks. Some recent efforts, such as the skip-gram model, have attempted to learn word representations that can capture both syntactic and semantic information among text corpus. However, they still lack the capability of encoding the properties of words and the complex relationships among words very well, since text itself often contains incomplete and ambiguous information. Fortunately, knowledge graphs provide a golden mine for enhancing the quality of learned word representations. In particular, a knowledge graph, usually composed by entities (words, phrases, etc.), relations between entities, and some corresponding meta information, can supply invaluable relational knowledge that encodes the relationship between entities as well as categorical knowledge that encodes the attributes or properties of entities. Hence, in this paper, we introduce a novel framework called RC-NET to leverage both the relational and categorical knowledge to produce word representations of higher quality. Specifically, we build the relational knowledge and the categorical knowledge into two separate regularization functions, and combine both of them with the original objective function of the skip-gram model. By solving this combined optimization problem using back propagation neural networks, we can obtain word representations enhanced by the knowledge graph. Experiments on popular text mining and natural language processing tasks, including analogical reasoning, word similarity, and topic prediction, have all demonstrated that our model can significantly improve the quality of word representations.