We test a method for applying a network-based approach to the study of political attitudes. We use cognitive-affective mapping, an approach that visually represents attitudes as networks of concepts that an individual associates with a given issue. Using a software tool called Valence, we asked a sample of Canadians (n = 111) to draw a cognitive-affective map (CAM) of their views on the carbon tax. We treat these networks as a series of undirected graphs and examine the extent to which support for the tax can be predicted based on each graph's emotional and structural properties. We find evidence that the emotional but not the structural properties significantly predict individuals' attitudes toward the carbon tax. We also find associations between CAMs' structural properties (density and centrality) and several measures of political interest. Our results provide preliminary evidence for the efficacy of CAMs as a tool for studying political attitudes. The study data are available at https://osf.io/qwpvd/?view_only=6834a1c442224e72bf45e7641880a17f