Complex networks are important tools for analyzing the information flow in many aspects of nature and human society. Using data from the microblogging service Twitter, we study networks of correlations in the appearance of words from three different categories, international brands, nouns and US major cities. We create networks where the strength of links is determined by a similarity measure based on the rate of coappearance of words. In comparison with the null model, where words are assumed to be uncorrelated, the heavy-tailed distribution of pair correlations is shown to be a consequence of modules of words representing similar entities.