Social media data provide increasing opportunities for the automated analysis of large sets of textual documents. So far, automated tools have been developed either to account for the social networks among participants in the debates, or to analyze the content of these debates. Less attention has been paid to mapping cooccurrences of actors (participants) and topics (content) in online debates that can be considered as socio-semantic networks. We propose a new, automated approach that uses the whole matrix of co-addressed topics and actors for understanding and visualizing online debates. We show the advantages of the new approach with the analysis of two data sets: first, a large set of Englishlanguage Twitter messages at the Rio + 20 meeting, in June 2012 (72,077 tweets), and second, a smaller data set of Dutch-language Twitter messages on bird flu related to poultry farming in 2015-2017 (2,139 tweets). We discuss the theoretical, methodological, and substantive implications of our approach, also for the analysis of other social media data.