## 2 Community Detection across Space and Its Variation across Time
### Community Detection across Space
#### 2.2.2 Algorithm
In addition, the aggregation of regions in both of the two time periods seems to be more significant than those in the corresponding time periods with cell size 1000 m. At midnight, the study area was partitioned into three communities. Compared to the result with cell size 1000 m, the interaction between land uses was weakened at midnight with cell size 500 m, and the region was divided into two main parts: one part was merged into the community of the business district (green dots), and the other one was merged into the community of business district and residential areas (blue dots). In general, the communities with cell size 500 m can reveal more detailed information of aggregation of land uses. Figure 10: _Cont._

Figure 9: Spatially embedded networks for traffic flows in different time periods with cell size k = 500 m: (a) morning rush hour; (b) noon rush hour; (c) evening rush hour; (d) midnight. Using the GSMM method, we also calculated the similarity matrix, as presented in Figure 11. It can be observed that in the rush hours, the measured values with 500 m cell size were similar to those with 1000 m cell size. In addition, during the non-rush hours, the measured values with 500 m cell size were higher than the corresponding values with 1000 m cell size. The reason could be that, with the refining of space tessellation, more cells had traffic flows and the number of the matching cells across time increased. Specifically, the small size grid can capture the local interactions between regions, which were more regular in the non-rush hours than in the rush hours (see Figure 9). ### Algorithm Efficiency with Different Cell Sizes

The results above show the effect of different cell sizes on community detection. In order to further explore the algorithm efficiency with different cell sizes, we implemented the method with cell sizes of 500 m, 600 m, 700 m, 800 m, 900 m, and 1000 m.

Figure 11: Similarity of the community structures in different time periods with 500 m cell size. Figure 5:0 Communities in different time periods with cell size k = 500 m: (**a**) morning rush hour; (**b**) noon rush hour; (**c**) evening rush hour; (**d**) midnight. With the increase of cell size, the total running time decreased (Figure 12a), and when the cell size changed from 500 m to 700 m, the algorithm efficiency increased sharply. When the cell size changed from 700 m to 1000 m, the running time remained stable. The reason could be that the number of nodes decreased with the increase of cell size, and thus the algorithm cost less time during the clustering of nodes. Furthermore, when the cell size was larger than 700 m, the number of iterations in k-means algorithm did not change much, and thus the running time of the algorithm remained stable. In addition, as presented in Figure 12b, the running time of the algorithm changed across the time periods. In general, the running time of the algorithm in the rush hours (e.g., 7:00-9:00, 11:00-13:00, 18:00-20:00, 22:00-23:00) was larger than those in the other hours. The reason could be that the flow structures are more complex in rush hours. Figure 5:1 The algorithm efficiency with different cell sizes: (**a**) the total running time of the algorithm with different cell sizes, and (**b**) the running time of the algorithm in different time periods. ## 5 Conclusion and Future Directions

Based on the collective intra-city trips extracted from the emerging taxi GPS trajectory data, this paper explored network traffic flows towards a deep understanding of city structure. We introduced network science techniques (e.g., community detection) to reveal the regular patterns of traffic flows across space and time. More specifically, aiming at the connectivity, aggregation, and dynamic properties of transport system, we proposed a three level framework to explore the complex traffic network. It firstly partitions the study region and constructs a spatially embedded network for representing the connectivity relationships between local regions.