This paper presents an empirical evaluation of state-of-the-art visualization techniques that combine Euler diagrams and graphs to visualize sets and networks. Focusing on SetNet, Bubble Sets and WebCola – techniques for which there is freely available software – our evaluation reveals that they can inaccurately and ineffectively visualize the data. Inaccuracies include placing vertices in incorrect zones, thus incorrectly conveying the sets in which the represented data items lie. Ineffective properties, which are known to hinder cognition, include drawing Euler diagrams with extra zones or graphs with large numbers of edge crossings. The results demonstrate the need for improved techniques that are more accurate and more effective for end users.