Assessing the Suitability of Fractal Dimension for Measuring Graphic Complexity Change in Schematic Metro Networks

Abstract

Schematization is a process of generating schematic network maps (e.g., metro network maps), where the graphic complexity of networks is usually reduced. In the past two decades, various automated schematization methods have been developed. A quantitative and accurate description of the complexity variation in the schematization is critical to evaluate the usability of schematization methods. It is noticed that fractal dimension (F) has been widely used to analyze the complexity of geographic objects, and this indicator may be appropriate for this purpose. In some existing studies, although F has been employed to describe the complexity variation, the theoretical and experimental basis for adopting this approach is inadequate. In this study, experiments based on 26 Chinese cities’ metro networks showed that the F of all these metro networks have decreased in schematization, and a significant positive correlation exists between the F of original networks and the reduction of F after schematization. The above results were verified to have similar trends with the subjective opinions of participants in a psychological questionnaire. Therefore, it can be concluded that F can quantitatively measure the complexity change of networks in schematization. These discoveries provide the basis for using F to evaluate the usability of schematization methods.