Abstract diagrams are powerful tools for comprehension and problem solving in diverse contexts. Two studies examined the structural properties of (i.e., applicability conditions for) three interrelated spatial diagrams—hierarchies, matrices, and networks. College students from two groups with distinct educational backgrounds and learning histories—advanced computer science students and representative undergraduates—rated the diagnosticity of the hypothesized applicability conditions for each of the 3 diagrams. The results validated 24–26 of the 30 hypothesized applicability conditions and provided evidence regarding the relative importance, or diagnosticity, of the validated properties for each type of diagram. A different set of properties was identified as most highly diagnostic for each type of diagram, indicating that the three spatial diagrams are optimized to serve different representational functions: The matrix stores static information about the kind of relation that exists between pairs of items in different sets, the network conveys dynamic information by showing the local connections and global routes connecting the items being represented, and the hierarchy depicts a rigid structure of power or precedence relations among items. The quantitative and qualitative differences in representational knowledge due to educational background are discussed.
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