This paper introduces Connected Concept Analysis (CCA) as a framework for text analysis which ties qualitative and quantitative considerations together in one unified model. Even though CCA can be used to map and analyze any full text dataset, of any size, the method was created specifically for taking the sensibilities of qualitative discourse analysis into the age of the Internet and big data. Using open data from a large online survey on habits and views relating to intellectual property rights, piracy and file sharing, I introduce CCA as a mixed-method approach aiming to bring out knowledge about corpuses of text, the sizes of which make it unfeasible to make comprehensive close readings. CCA aims to do this without reducing the text to numbers, as often becomes the case in content analysis. Instead of simply counting words or phrases, I draw on constant comparative coding for building concepts and on network analysis for connecting them. The result - a network graph visualization of key connected concepts in the analyzed text dataset - meets the need for text visualization systems that can support discourse analysis.