In his book Multimedia Learning [7], Richard Mayer asserts that viewers learn best from imagery that provides them with cues to help them organize new information into the correct knowledge structures. Designers have long been exploiting the Gestalt laws of visual grouping to deliver viewers those cues using visual hierarchy, often communicating structures much more complex than the simple organizations studied in psychological research. Unfortunately, designers are largely practical in their work, and have not paused to build a complex theory of structural communication. If we are to build a tool to help novices create effective and well structured visuals, we need a better understanding of how to create them. Our work takes a first step toward addressing this lack, studying how five of the many grouping cues (proximity, color similarity, common region, connectivity, and alignment) can be effectively combined to communicate structured text and imagery from real world examples. To measure the effectiveness of this structural communication, we applied a digital version of card sorting, a method widely used in anthropology and cognitive science to extract cognitive structures. We then used tree edit distance to measure the difference between perceived and communicated structures. Our most significant findings are: 1) with careful design, complex structure can be communicated clearly; 2) communicating complex structure is best done with multiple reinforcing grouping cues; 3) common region (use of containers such as boxes) is particularly effective at communicating structure; and 4) alignment is a weak structural communicator.