## 3 Results
### Relationships between Retail Store Locations and Weighted Centrality from a Temporal Perspective  
This section examines how the density distribution of retail stores may correlate with the weighted centrality indices. First, the flow network without temporal division is examined, which is constructed by the total public transit flows of the whole week. Table 3 shows the highest correlation coefficients between various retail stores and weighted centrality indices. Pearson's correlation analysis was conducted between the density of retail stores and weighted centrality indices. Figure 6: Spatial distributions of weighted degree centrality indices on weekdays: (**a**) degree, 7:00–9:00; (**b**) degree, 11:00–13:00; (**c**) degree, 19:00–21:00; (**d**) betweenness, 7:00–9:00; (**e**) betweenness, 11:00–13:00; (**f**) betweenness, 19:00–21:00; (**g**) closeness, 7:00–9:00; (**h**) closeness, 11:00–13:00; (**i**) closeness, 19:00–21:00. First, most store types have rather high correlation coefficients with weighted centrality indices. Convenience stores, shopping malls, supermarkets, and electronics stores have strong correlations with all weighted centrality indices, with coefficients above 0.6. The highest correlation coefficients for each type of store are more than 0.7, and the highest coefficient is achieved by convenience stores (with values above 0.8). Specialty stores have the highest coefficient, exceeding 0.5. Only building material stores exhibit weak correlations with weighted centrality indices (the highest coefficient is less than 0.4), which \begin{table}
\begin{tabular}{c c c c} \hline
**Retail Types** & **Degree** & **Betweenness** & **Closeness** \\ \hline Shopping malls & 0.770 & 0.785 & 0.580 \\ Supermarkets & 0.722 & 0.625 & 0.718 \\ Convenience stores & 0.812 & 0.747 & 0.740 \\ Electronics stores & 0.716 & 0.636 & 0.685 \\ Specialty stores & 0.553 & 0.485 & 0.413 \\ Building material stores & 0.261 & 0.211 & 0.371 \\ \hline \end{tabular}
\end{table} 
Table 3: Correlation coefficients of KDE values of stores and weighted centrality indices of total flow network. Figure 7: Spatial distributions of weighted degree centrality indices on weekends: (**a**) degree, 7:00–9:00; (**b**) degree, 11:00–13:00; (**c**) degree, 19:00–21:00; (**d**) betweenness, 7:00–9:00; (**e**) betweenness, 11:00–13:00; (**f**) betweenness, 19:00–21:00; (**g**) closeness, 7:00–9:00; (**h**) closeness, 11:00–13:00; (**i**) closeness, 19:00–21:00.  
is consistent with the previous findings by using street centrality indices [22; 23; 24], which implies that building material stores may be relatively less correlated to the public transport flow. These results indicate that most of the six types of retail stores are highly correlated to weighted centralities in the public transport flow network. Second, four types, namely, supermarkets, convenience stores, electronics stores, and specialty stores, show the highest correlations with weighted degree. Only shopping malls show the highest correlation coefficients with weighted betweenness, with the highest correlation coefficient value reaching 0.785. This finding indicates that high-grade retail stores prefer nodes that are included in paths with relatively large flows. In comparison, it has been reported that betweenness performs well in previous physical street network studies [18; 22; 23; 24]. This is also consistent with our findings, as betweenness in street networks reflects the frequency of the shortest paths passing through, while the weighted degree in this study directly reflects public traffic volume. The results indicate that transport volume has a significant impact on the location patterns of retail stores. Then, the flow networks for different periods of a day with a distinction between weekdays and weekends are examined. Tables 4-6 show the temporal analysis results.