## 3 Results
### Relationships between Retail Store Locations and Weighted Centrality from a Temporal Perspective
Only the index type of specialty stores changes in degree on weekdays to betweenness on weekends, but its correlations are less than 0.7. It is noteworthy that the three types of shopping malls, supermarkets, and convenience stores sell general commodities but differ in store size and diversity in their commodity types. For these three types, they all nearly achieve the highest correlations during the period of 19:00-21:00 for the whole week, while the only outlier is that the shopping mall type correlates more strongly to a different period of 11:00-13:00 on weekends. The same period implies that most consumers go shopping after work, but shopping behavior for malls on weekends may differ, as people may like to spend time in malls. Another interesting result for the three types is that the highest centrality indices are different: convenience stores correlate best with degree, supermarkets correlate best with closeness, and shopping malls correlate best with betweenness. Recall that for the total flow network without periods in Table 3, the highest centrality index for the supermarket changed here from degree to closeness. In this case, the results of the total flow network may be misleading. Moreover, recall that the degree reflects the total traffic flow, the closeness reflects the closeness to all nodes in the flow network, and the betweenness reflects the traffic corridor. Thus, it can be inferred that the higher levels of store types are associated with higher correlations to the key structure of the flow network. For the two types of specialty stores and electronics stores, both correlate best to degree centrality on weekdays, and neither correlate best with the period of 19:00-21:00 on weekends. These results imply that people may visit these types of stores after work on weekdays and may visit them at various periods in the daytime on weekends. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Store Types**} & \multicolumn{3}{c}{**Weekdays**} & \multicolumn{3}{c}{**Weekends**} \\ \cline{2-6}  & **Period** & **Centrality** & **Coefficient** & **Period** & **Centrality** & **Coefficient** \\ \hline Shopping malls & 19:00–21:00 & Betweenness & 0.815 & 11:00–13:00 & Betweenness & 0.769 \\ Supermarkets & 19:00–21:00 & Closeness & 0.750 & 19:00–21:00 & Closeness & 0.752 \\ Convenience stores & 19:00–21:00 & Degree & 0.812 & 19:00–21:00 & Degree & 0.820 \\ Specialty stores & 11:00–13:00 & Degree & 0.563 & 13:00–15:00 & Betweenness & 0.587 \\ Electronics stores & 19:00–21:00 & Degree & 0.721 & 7:00–9:00 & Degree & 0.733 \\ Building material stores & 7:00–9:00 & Closeness & 0.373 & 7:00–9:00 & Closeness & 0.375 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Highest correlation coefficients of all periods. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**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{4}{*}{betweenness} & Shopping mall & 0.752 & 0.758 & 0.769 & 0.753 & 0.729 & 0.766 & 0.769 \\  & Supermarket & 0.688 & 0.694 & 0.703 & 0.655 & 0.639 & 0.667 & 0.694 \\  & Convenience store & 0.765 & 0.776 & 0.790 & 0.754 & 0.734 & 0.770 & 0.777 \\  & Specialty store & 0.486 & 0.504 & 0.556 & 0.587 & 0.581 & 0.564 & 0.519 \\  & Electronics store & 0.672 & 0.677 & 0.685 & 0.644 & 0.630 & 0.657 & 0.683 \\  & Building material store & 0.266 & 0.267 & 0.266 & 0.220 & 0.213 & 0.226 & 0.256 \\  & Shopping mall & 0.577 & 0.588 & 0.601 & 0.610 & 0.622 & 0.624 & 0.640 \\  & Supermarket & 0.726 & 0.728 & 0.735 & 0.740 & 0.744 & 0.744 & 0.752 \\  & Convenience store & 0.745 & 0.749 & 0.758 & 0.764 & 0.770 & 0.771 & 0.783 \\  & Specialty store & 0.413 & 0.423 & 0.433 & 0.441 & 0.451 & 0.451 & 0.460 \\  & Electronics store & 0.688 & 0.691 & 0.699 & 0.704 & 0.710 & 0.711 & 0.719 \\  & Building material store & 0.375 & 0.368 & 0.367 & 0.366 & 0.364 & 0.366 & 0.366 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._