## 5 Conclusions  
In light of the growing focus on China's transportation network development and city cluster economy, this research investigates the spatial distribution of intercity transportation efficiency for automobiles and trains within China's city clusters. The study focuses on the scale of the city cluster, aiming to address the existing research gap in this area. This contribution can offer theoretical insights for future urban planning endeavors. The variations in transportation network density, diverse geometric properties of networks, and differences in population distribution among various cities result in discrepancies in transportation efficiency across urban areas. An extended concept of circuity is proposed to address the limitations of the original circuity, which primarily emphasizes the distance dimension, while overlooking the speed of different modes of transportation and road conditions. It encompasses the temporal aspect and is commonly known as the speed of the transportation network. FWTC is proposed through the integration of transportation network speed and the gravity model. This approach aims to provide a more accurate assessment of intercity transportation efficiency. Furthermore, the study focuses on seven major city clusters in China; data on navigation for automobile and train travel modes are collected using Amp's API. Real-time data enables the analysis of travel time between city pairs, facilitating an examination of spatial patterns in intercity transportation efficiency for both automobile and train travel modes within China's city clusters. The results indicated the following:  
(1) As the Euclidean distance between the origin and destination cities increases, there is a rising trend in the average of transportation network travel speed. However, the level of fluctuation also intensifies. From the standpoint of various transportation modes, as the Euclidean distance between the cities of origin and destination expands, the discrepancy in travel speed within the transportation network between train and automobile gradually decreases. In the context of variability, train travel demonstratesmore significant fluctuations, while automobile travel shows a higher level of stability, characterized by more concentrated data points. (2) In terms of the city cluster scale, the speed of automobile travel within the transportation network is faster and more evenly distributed, resulting in fewer disparities among various city clusters. In terms of transportation network travel speed by train, the Yangtze River Delta and Beijing-Tianjin-Heibei regions demonstrate a relatively superior performance compared to the relatively inferior performance of the Pearl River Delta and Guanzhong Plain. (3) The intercity efficiency of automobile travel is typically high within each city cluster, with the exception of the Guanzhong Plain. The Yangtze River Delta and Beijing-Tianjin-Heibei regions exhibit a particularly noteworthy performance in this regard. From the standpoint of intercity train travel efficiency, the Yangtze River Delta, Beijing-Tianjin-Heibei, and Mid-Yangtze River regions demonstrate significant efficiency owing to their interconnected train networks. In contrast, the Guanzhong Plain exhibits a relatively lower efficiency in its train traffic, highlighting the necessity for additional development and enhancement. Overall, the benefits of intercity travel by car are more pronounced when considered on a city cluster scale. While intercity train travel presents a significant advantage in regions where the Euclidean distance between the originating and destination cities exceeds 300 km, there is still a need for overall improvement in its efficiency. The study has several limitations. Firstly, the selection of the origin and destination for intercity travel typically focuses on the most representative locations within the city, rather than employing an extensive sampling of points to accurately simulate real travel conditions.