## 1 Introduction
### Research Objectives and Structure  
The literature review reveals that numerous scholars have dedicated their efforts to investigating the effectiveness of intercity transportation networks, providing the groundwork for this study. However, there are still disadvantages in certain areas, primarily in the following areas:  
(1) The conventional distance-based circuity remains predominant in the realm of transportation network efficiency research [18; 20; 28; 29]. However, this indicator fails to account for the travel mode and the volume of travel. While there have been efforts to broaden its scope by incorporating travel time, the methodology remains underdeveloped and is unable to provide an accurate assessment of the effectiveness of intercity transportation networks.  
(2) Contemporary research on travel efficiency predominantly employs aggregation techniques to assess the travel efficiency of a particular transportation mode within an urban area [16; 19; 26; 28; 33]. Alternatively, the operational efficiency of a specific road network type at the national level is taken into consideration [14; 20; 29]. At this stage, urban agglomerations' economy has emerged as the predominant mode of economic development. The absence of thorough efficiency studies comparing various modes of transportation within city clusters hinders the advancement of intercity transport in city clusters towards a more sustainable and cost-effective direction.  
In summary, this study provides a new definition of distance-based circuity by incorporating travel time considerations. Subsequently, it was integrated with the gravity model to introduce a novel framework for assessing the efficiency of intercity transportation. Taking into account the travel mode and traffic flows, this approach can provide a more accurate description of the effectiveness of the intercity transportation network. The efficiency examined in this research emphasizes the significance of the intercity transportation network within a local area, for the functioning of the intercity transportation network across the entire urban cluster, as opposed to solely assessing the accessibility or convenience of a specific road segment.  
Subsequently, real-time navigation information for car and train travel between cities is acquired using Amap's API. This study examines the spatial distribution of transportation efficiency among various intercity travel modes within seven major city clusters in China. By comparing the traffic efficiency of different regions, the effectiveness of infrastructure construction can be verified, so as to ensure the low energy consumption of the whole process of the construction and operation of the transportation network to the maximum extent.  
The analysis is carried out at the level of city clusters and the research results are also accompanied by a discussion of their policy implications. The subsequent sections of the paper are structured as follows: In Section 1, the background, the related studies, and the main work of this research have been introduced in detail. The methodology and the techniques for data processing and data acquisition are presented in Section 2. The results are outlined in Section 3, which is followed by a discussion in Section 4. Section 5 serves as the conclusion of this study.