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We present a study of the relationship between gender, linguistic style, and social networks, using a novel corpus of 14,000 Twitter users. Prior quantitative work on gender often treats this social variable as a female/male binary; we argue for a more nuanced approach. By clustering Twitter users, we find a natural decomposition of the dataset into various styles and topical interests. Many clusters have strong gender orientations, but their use of linguistic resources sometimes directly conflicts with the population-level language statistics. We view these clusters as a more accurate reflection of the multifaceted nature of gendered language styles. Previous corpus-based work has also had little to say about individuals whose linguistic styles defy population-level gender patterns. To identify such individuals, we train a statistical classifier, and measure the classifier confidence for each individual in the dataset. Examining individuals whose language does not match the classifier's model for their gender, we find that they have social networks that include significantly fewer same-gender social connections and that, in general, social network homophily is correlated with the use of same-gender language markers. Pairing computational methods and social theory thus offers a new perspective on how gender emerges as individuals position themselves relative to audiences, topics, and mainstream gender norms., Comment: submission version