## 3 Results
### Relationships between Retail Store Locations and Weighted Centrality from a Temporal Perspective
Tables 4 and 5 show the correlation coefficients to the three weighted centrality indices across store types at different periods, and Table 6 shows the highest correlation coefficients for each store type across the periods of a day and the relative centrality indices. Tables 4 and 5 indicate that correlation coefficients vary across the day. For the relationship between weighted closeness and most retail stores on weekends, there is a continuous slight upward trend in the correlation coefficients with time. The relationships between the weighted degree and building material stores on weekdays are high in the morning and evening and low at noon. However, for the weighted degrees among specialty stores on weekdays, this pattern is reversed. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Centrality** & **Retail Types** & **7:00–9:00** & **9:00–11:00** & **11:00–13:00** & **13:00–15:00** & **15:00–17:00** & **17:00–19:00** & **19:00–21:00** \\ \hline \multirow{6}{*}{degree} & Shopping mall & 0.763 & 0.786 & 0.775 & 0.772 & 0.768 & 0.768 & 0.784 \\  & Supermarket & 0.723 & 0.711 & 0.717 & 0.714 & 0.718 & 0.717 & 0.718 \\  & Convenience store & 0.807 & 0.810 & 0.812 & 0.809 & 0.809 & 0.808 & 0.812 \\  & Specialty store & 0.545 & 0.546 & 0.562 & 0.563 & 0.561 & 0.552 & 0.538 \\  & Electronics store & 0.715 & 0.711 & 0.710 & 0.708 & 0.709 & 0.710 & 0.721 \\  & Building material store & 0.266 & 0.253 & 0.252 & 0.248 & 0.253 & 0.257 & 0.264 \\  & Shopping mall & 0.771 & 0.786 & 0.814 & 0.811 & 0.815 & 0.754 & 0.775 \\  & Supermarket & 0.643 & 0.615 & 0.637 & 0.635 & 0.648 & 0.572 & 0.605 \\  & Convenience store & 0.751 & 0.738 & 0.762 & 0.763 & 0.774 & 0.710 & 0.724 \\  & Specialty store & 0.473 & 0.460 & 0.506 & 0.511 & 0.515 & 0.443 & 0.453 \\  & Electronics store & 0.638 & 0.620 & 0.650 & 0.643 & 0.656 & 0.581 & 0.618 \\  & Building material store & 0.222 & 0.215 & 0.215 & 0.208 & 0.220 & 0.177 & 0.204 \\  & Shopping mall & 0.570 & 0.589 & 0.611 & 0.616 & 0.628 & 0.622 & 0.640 \\  & Supermarket & 0.715 & 0.727 & 0.741 & 0.744 & 0.748 & 0.742 & 0.750 \\  & Convenience store & 0.733 & 0.749 & 0.766 & 0.770 & 0.776 & 0.769 & 0.783 \\  & Specialty store & 0.406 & 0.420 & 0.439 & 0.443 & 0.454 & 0.444 & 0.455 \\  & Electronics store & 0.680 & 0.691 & 0.704 & 0.708 & 0.713 & 0.709 & 0.718 \\  & Building material store & 0.373 & 0.372 & 0.369 & 0.371 & 0.368 & 0.371 & 0.368 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Correlation coefficients of KDE values of stores and weighted centrality indices for each period on weekdays. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Centrality** & **Retail Types** & **7:00–9:00** & **9:00–11:00** & **11:00–13:00** & **13:00–15:00** & **15:00–17:00** & **17:00–19:00** & **19:00–21:00** \\ \hline \multirow{6}{*}{degree} & Shopping mall & 0.747 & 0.747 & 0.742 & 0.747 & 0.750 & 0.750 & 0.763 \\  & Supermarket & 0.749 & 0.733 & 0.724 & 0.719 & 0.720 & 0.727 & 0.734 \\  & Convenience store & 0.817 & 0.811 & 0.806 & 0.805 & 0.806 & 0.810 & 0.820 \\  & Specialty store & 0.540 & 0.554 & 0.559 & 0.563 & 0.564 & 0.557 & 0.550 \\  & Electronics store & 0.733 & 0.717 & 0.712 & 0.709 & 0.709 & 0.719 & 0.727 \\  & Building material store & 0.294 & 0.270 & 0.260 & 0.253 & 0.253 & 0.266 & 0.277 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Correlation coefficients of KDE values of stores and weighted centrality indices for each period on weekends. Table 6 shows that most of the highest correlation coefficients are rather large both on weekends and on weekdays. Compared with the results for the total flow network (Table 3), the values of the highest correlation coefficients here are larger, which means that analyses without time divisions may underestimate correlations. For the same store types, most types, except for shopping malls, have higher correlations on weekends. Most types show consistency in a preference for the highest centrality index from weekdays to weekends.