## 2 Community Detection across Space and Its Variation across Time
### Community Detection across Space
#### 2.2.2 Algorithm
Secondly, most of the community structures in the rush hours (e.g., the similarity between [7:00-8:00] and [8:00-9:00]) had a high similarity. Hence, the distributions of traffic flows are so regular in these periods that urban planners could estimate the associated travel behavior patterns. Note that the community structures between [12:00-14:00] and [4:00-7:00] were similar at the macro scale. Considering the routines and habits of residents, there are relatively few traffic flows in these periods and the arterial roads provide the main functions of transportation in the city. The travel origins and destinations are concentrated in a few business districts and railway stations. Hence, the traffic conditions in these time periods showed a similar characteristic. In addition, it can be observed that the community structure in [21:00-22:00] was very different from most of the structures in the other time periods. The reason may be that there are many different activities happening (e.g., working and entertainment) in [21:00-22:00], and thus the connectivity between local regions is much more complex than those in other time periods. Furthermore, the community structure in the evening rush hour of [18:00-19:00] was also very different from most of the other structures. This could be because in this time period the travel activities become increasingly active, and most of the residents in Beijing choose to travel along different routes. The land uses were also aggregated into different communities in this period compared to those in the successive time periods. ### Variation in Different Spatial Scales

Our proposed method is adaptive to applications with different spatial scales. Hence, the next experiment refined the tessellation of space using a 500 m grid and analyzed the associated spatial community patterns across space and time. As the size of cells becomes smaller, there are more cells with no nodes, which correspond to the buildings (e.g., Imperial Palace) or lakes (e.g., Beihai Park) (Figure 9). We can easily observe the distributions of these land uses from the spatially embedded networks. In addition, compared to networks with 1000 m cell size, networks with 500 m cell size can present more detailed structures of street network infrastructure and associated traffic flows in the city. With the refined tessellation, we could observe more detailed interactions from the results. In the morning rush hour, strong connectivity existed mainly among the regions of residential areas, business districts, and high-tech areas. Entering the noon rush hour, the ring-like structure of the transport system became most significant. In addition, in the periods of the evening rush hour and midnight, the traffic flows were concentrated in the eastern and northern parts, which are the business cores of the city. Therefore, the transport system of Beijing depends largely on the loop lines, with a significant temporal pattern. Figure 8: Similarity of the community structures in different time periods with 1000 m cell size. Figure 9: _Cont._In order to compare the results under the two scales, we also classified the land uses into eight communities. As presented in Figure 10a, the study region was partitioned into three main communities in the morning rush hour. The eastern region was divided into two parts, and the community represented by green dots implies the aggregation of residential area (i.e., western part) and commercial business districts (i.e., eastern part). Another part in the eastern region was merged with the northern region, and the resulting community implies the aggregation of residential areas, universities, and high-technology regions. Later, entering the noon rush hour and the evening rush hour, the study region was partitioned into three communities and four communities, respectively.