## 1 Introduction  
The objective measurement of spatial information in maps is an important branch of cartographic theoretical research, which helps map users and cartographers gain a more general understanding of map content, and a more detailed understanding of the richness of map data and the spatial distribution of map information [1; 2; 3]. The measurement of the spatial information content in maps is a crucial issue for effectively perceiving and understanding map data, playing a fundamental role in cognitive understanding in scientific research related to cartography [4]. The study of spatial information in maps encompasses both qualitative and quantitative research aspects. Qualitative research primarily focuses on evaluating the quality of data, while quantitative research focuses on the amount of information contained in the data. These two aspects represent two dimensions of map data description [5]. The quantitative study of spatial information in maps encompasses various aspects such as the definition, expression, and measurement of information, constituting a comprehensive and systematic research project. Due to the involvement of various disciplinary systems and specific applications in the measurement of semantic information of maps [6; 7; 8; 9], it is currently difficult to establish an effective semantic information measurement system that is suitable for multiple application needs. Therefore, the scope of this study temporarily excludes the measurement of semantic information of maps and focuses instead on spatial information that is commonly considered by the majority of map users. Spatial information in map data refers to the information expressed by the geometric characteristics of map objects and the spatial distribution characteristics among map objects [10]. Based on previous research, this study further defines spatial information in map data as the degree of diversity represented by the geometric characteristics of map objects and the degree of spatial distribution diversity characterized by the diverse spatial distribution characteristics among map objects. The spatial information of maps observable by users is jointly composed of the interaction between these two types of information. Currently, most research focuses on a specific aspect of spatial information in maps, such as geometric information [11; 12; 13], spatial distribution information [14; 15], and thematic attribute information [8; 9]. There is relatively less quantitative research on systematic spatial information in maps [5; 16; 17]. However, imagining the distribution patterns of map objects while ignoring the geometric shapes of objects requires high-level, abstract, and generalizing abilities. As a result, map users and cartographers typically focus on the overall and systematic aspects of maps. Therefore, a comprehensive measurement of spatial information content in maps is necessary and important. In the current era of the continuous generation, accumulation, and updating of map data, the measurement of spatial information content in maps will greatly reduce the high costs and subjectivity associated with expert experience and manual discrimination, thereby enhancing the utilization efficiency of map data. Currently, only [PERSON] et al. and [PERSON] et al. have proposed systematic methods for the quantitative measurement of spatial information content in maps [16; 17]. However, their methods fail to effectively consider the diversity of adjacency relationships and the heterogeneity of distance relationships among area objects, which affect the accuracy and objectivity of the measurement results of map information. Therefore, it is necessary to conduct further research on the systematic measurement of spatial information content in maps and propose a more theoretically comprehensive measurement method.