Production and Comprehension of Structured Graphs based on Knowledge Space Theory

In this project, we investigated human comprehension of visualized ordered sets. Ordered sets provide a non-numerical data structure, whose mathematical properties are very general. Therefore, they appear in many contexts in which ordered information is processed.

An outstanding feature of ordered sets is that they can be visualized by means of so-called upward drawings or Hasse diagrams. Such drawings can provide easy access to the ordering information. Therefore, ordered sets and their visualizations play an important role in the (computer-aided) visual presentation of ordered information. There is a great interest in criteria for `good’ drawings, i.e., for drawings which are easy to comprehend.

The visualization of ordered sets in upward drawings is not unique. In the mathematical and computer scientific literature, several mathematical properties referring to ordered sets are applied to upward drawings. This is done in order to provide criteria for what a good drawing should look like. The most prominent visual properties are planarity, slopes and levels. In a series of experiments the influence of these properties on speed of comprehension and their adequate visualization in respective drawings were systematically investigated. Upward drawings were presented to participants together with interpretive questions. Participants’ answers to these questions and the respective latencies were analyzed.

We found out that planarity is the most important property with respect to speed of comprehension, irrespective of other properties of a drawing. If the interpretive questions are more demanding, then slopes have a substantial influence on speed of comprehension too. The more demanding the information is that a reader has to extract from a drawing, the greater is the influence of the visual properties. Our results are of interest to anybody involved in the professional design and display of ordered information.


Duration: 01.03.1997 – 01.12.1998 (22 months)

Funding: Supported by Austrian National Bank (Jubiläumsfonds). Grant No.: 6227