# Detecting Urban Mobility Structure and Learning Functional Distribution with Multi-Scale Features
## 4 Case Study
### Urban Mobility Structure Detection  
Based on the embedding of urban mobility structures, we divided the urban regions of weekdays and weekends into five communities. The number of each community is shown in Table 3, and the spatial distribution is depicted in Figure 6. Although there are different travel demands on weekdays and weekends, it can be observed that the spatial distribution of different community types is generally similar for both weekdays and weekends. This is because Haikou City has a single-center structure. The central urban area, as the core of the city, integrates multiple functions such as commerce, culture, and administration and has a large flow of activities. Type I communities are primarily located in areas such as Hainan University, Hainan Normal University, Sunshine City, and Haikou East Station, mainly serving higher education, shopping centers, and transportation hubs, representing the core area of Haikou City. The distribution of Type II communities is mainly  
Figure 5: Study area.  
adjacent to Type I, primarily located around Haikou Station, residential areas, and wellness and vacation parks, representing the sub-central areas of Haikou City. Type III, Type IV, and Type V communities are primarily distributed in suburban areas and regions with lower population density. However, on weekends, the community classification of certain industrial and residential areas located farther from the city center shifts from Type I and Type II, observed on weekdays, to Type III or Type IV. This shift occurs as residents' travel patterns transition from work-related commuting to leisure and recreational activities, leading to diminished connectivity between these areas and the central regions.  
Figure 6: Division of community structure.  
We selected Louvain and GCL as baseline models and quantitatively compared the results of urban mobility structure partitioning. The Louvain algorithm treats different areas or nodes of the city as vertices in a graph, with edges between the vertices representing the flow between regions. By aggregating vertices, the Louvain algorithm can effectively identify areas in the city with similar activity patterns. However, it cannot account for edge weights and the direction of flow. GCL, on the other hand, first generates sample pairs through a graph augmentation strategy, then uses a graph neural network encoder for contrastive learning of node embedding representations. It applies clustering algorithms to group the node embeddings and identify different communities within the city. However, GCL cannot learn global activity structure features.  
The results of urban mobility structure partitioning are measured by edge density, which is the ratio of the actual number of edges present in each community to the maximum number of edges that can be accommodated, as follows:  
\[\rho\ =\ \sum_{k=1}^{K}\frac{E(C_{k})}{K|C_{k}|(|C_{k}|-1)} \tag{14}\]  
where \(E(C_{k})\) is the number of edges in community \(C_{k}\), and \(|C_{k}|(|C_{k}|-1)\) is the maximum number of edges.  
The edge density results are shown in Table 4. A higher edge density indicates that the regions are more closely connected, suggesting better urban mobility structure partitioning. The edge density indicator of the proposed method is the highest on both weekdays and weekends, indicating that the method can effectively leverage multi-scale features to improve the validity of community partitioning. However, among the three methods, the edge density on weekends is lower than on weekdays. This is because, on weekends, people have more diverse travel demands, leading to increased connections between different communities, which makes urban mobility structure partitioning more challenging.