In recent years, concepts and methods of complex networks have been employed to tackle the word sense disambiguation (WSD) task by representing words as nodes, which are connected if they are semantically similar. Despite the increasingly number of studies carried out with such models, most of them use networks just to represent the data, while the pattern recognition performed on the attribute space is performed using traditional learning techniques. In other words, the structural relationship between words have not been explicitly used in the pattern recognition process. In addition, only a few investigations have probed the suitability of representations based on bipartite networks and graphs (bigraphs) for the problem, as many approaches consider all possible links between words. In this context, we assess the relevance of a bipartite network model representing both feature words (i.e. the words characterizing the context) and target (ambiguous) words to solve ambiguities in written texts. Here, we focus on the semantical relationships between these two type of words, disregarding the relationships between feature words. In special, the proposed method not only serves to represent texts as graphs, but also constructs a structure on which the discrimination of senses is accomplished. Our results revealed that the proposed learning algorithm in such bipartite networks provides excellent results mostly when topical features are employed to characterize the context. Surprisingly, our method even outperformed the support vector machine algorithm in particular cases, with the advantage of being robust even if a small training dataset is available. Taken together, the results obtained here show that the proposed representation/classification method might be useful to improve the semantical characterization of written texts.