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

Author:

Lan Tian1ORCID,Wu Zhiwei1ORCID,Sun Chenzhen1,Cheng Donglin1,Shi Xing1,Zeng Guangjun1,Zhang Hong23,Peng Qian4ORCID

Affiliation:

1. Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, China

2. School of Geographic Sciences, East China Normal University, Shanghai 200241, China

3. Institute for Global Innovation and Development, East China Normal University, Shanghai 200062, China

4. Faculty of Resources and Environmental Science, Hubei University, Wuhan 430062, China

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.

Funder

National Natural Science Foundation of China

National Key Research and Development Program of China

Publisher

MDPI AG

Subject

Earth and Planetary Sciences (miscellaneous),Computers in Earth Sciences,Geography, Planning and Development

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