## 2 Community Detection across Space and Its Variation across Time
### Community Detection across Space
#### 2.2.2 Algorithm
The total number of valid records was more than 20,000,000, which covers a time period of 24 h (from 0 a.m. to 12 p.m.) (Figure 4). Because of signal loss or degradation, geospatial locations of trajectory may have been recorded with spatial and temporal uncertainties. Considering these factors, our data were preprocessed by the provider to indicate whether the record was valid or invalid with respect to the GPS signal. In our research, only the valid records were used. Nevertheless, there were some small deviations in position information relative to the actual position. In this respect, we adopted the technique of region tessellation, which is used to model collective behaviors between regions. The internal variation of the region is not considered. Hence, it can handle small deviations of location information and can be used to reveal the collective travel patterns between regions. In order to have a macroscopic understanding of people's travel patterns, we extracted the taxi pick-up and drop-off points (Figure 5). It can be observed that the hotspots of pick-up and drop-off points are distributed within the second ring roads of Beijing. ## 4 Experiment and Result

### Result and Analysis

We first partitioned the study area into a set of cells with size \(1\) km \(\times\)\(1\) km. This scale was determined on the basis of relevant studies suggesting that the cell size is fine enough to depict urban structure [33]. We then used these cells to construct spatially embedded networks to analyze the

Figure 4: Study area: the core area of Beijing. Figure 5: Passengers pick-up/drop-off points. interactions between land uses (i.e., sub-regions). Moreover, we obtained the results in different time periods to discover the dynamic patterns of the transport system. In the spatially embedded network, the nodes represent the regions of the city and the edges represent the traffic linkage between different regions. Furthermore, the intensity of the connections between different regions varies with time. In order to clearly reveal the travel patterns, we constructed networks for typical time periods (Figure 6), i.e., morning rush hour, noon rush hour, evening rush hour, and midnight. During different time periods of the day, the traffic flows showed different spatial connectivity patterns to meet the varying travel demands of people. In the morning rush hour, the interactions between residential areas, working areas, and schools were more intense than those between the other areas. Later, entering the period of the noon rush hour, the traffic flow volume and the associated connectivity patterns became more significant in the central areas and main roads of the city. Most of the central areas belong to the working zone and commercial zone, and thus the strong connectivity indicates the frequent interactions between working and lunch activities. In addition, although the volume of traffic flows in the evening rush hour was less than that in morning rush hour, their network structures were similar. In Beijing, in order to avoid traffic congestions, many people choose to get off work and go home or go to recreational areas after 19:00. This may be a reason that the traffic

Figure 6: Spatially embedded networks for traffic flows in different time periods with cell size k = 1000 m: (**a**) morning rush hour; (**b**) noon rush hour; (**c**) evening rush hour; (**d**) midnight. volume in evening rush hour was less than that in morning rush hour. Additionally, the routes that people choose to go to work and get off work are similar, and thus the networks in the morning rush hour and evening rush hour had a similar structure. Furthermore, the networks at midnight had a multi-center structure, which depended on the hubs of recreational areas and commercial areas. In general, except the morning rush hour, the other time periods depended more on the eastern areas than the western areas. Among these hours, the noon rush hour had the largest volume of traffic flows.