Function word adjacency networks (WANs) are used to study the authorship of plays from the Early Modern English period. In these networks, nodes are function words and directed edges between two nodes represent the relative frequency of directed co-appearance of the two words. For every analyzed play, a WAN is constructed and these are aggregated to generate author profile networks. We first study the similarity of writing styles between Early English playwrights by comparing the profile WANs. The accuracy of using WANs for authorship attribution is then demonstrated by attributing known plays among six popular playwrights. Moreover, the WAN method is shown to outperform other frequency-based methods on attributing Early English plays. In addition, WANs are shown to be reliable classifiers even when attributing collaborative plays. For several plays of disputed co-authorship, a deeper analysis is performed by attributing every act and scene separately, in which we both corroborate existing breakdowns and provide evidence of new assignments.