## 3 Results
### Centrality Indices
#### 3.2.1 Global Centrality Results  
Figure 5 presents the results for global reach (GR), which represents the number of accessible villages for each origin. An increasing trend is found in most of the villages. However, Zhaili Town in the north and Liulizhuang Town in the south all maintained a low reach centrality across the years. In contrast, two other cases with similar locations--Dawang Town, which represents the only village cluster on the north border other than Zhaili Town, and Tongkou Town, just next to Liulizhuang Town--demonstrated rapid development from 1964 to 1996, as in 1996 they benefited from the construction of the Rongcheng-Lixian National Highway in the north and Gaoyang-Baoding Provincial Highway in the south, adjoining the county border. In this period, villages' global reach value in the south grew faster than in the north. However, from 1996 to 2008, this trend was reversed because of extensions to the road network around the county, as can be seen in Figure 4b.  
Figure 4: Changes in the road system of Anxin County between (**a**) 1964 and 1975 and (**b**) 1996 and 2008.  
Figure 6 presents the results for global betweenness (GB), indicating the likelihood of the village being passed through in the road system. In 1964, the intermediation role of semi-waterside villages was strong, but this advantage gradually disappeared from 1996 to 2008. In 1996, the villages on the north and south edge and along the Baoding-Anxin Provincial Highway had relatively strong intermediation, and this trend became pronounced in 2008. The villages around the county center had a strong intermediation role due to the extension of the road network in 2008.  
Figure 7 presents the results for global closeness (GC), indicating the geographical proximity of a village to other villages within a certain range. The closeness centrality results show opposite characteristics to those of the other parameters. Villages in Liulizhuang Town, which maintained a low value for other centrality metrics, had high closeness with neighboring villages. This suggests that this town had strong internal cohesion but a weak correlation with other towns. However, most other villages maintained a low closeness value.  
Figure 8 shows the results for global gravity (GG), indicating the gravitational pull of a village on other villages within a certain range. High-GG villages that appear in clusters show strong interaction forces. In 1964, high-GG villages were all semi-waterside villages. After the completion of the modern road network in 2008, high-GG villages became more numerous, and most of them overlapped with township centers.  
Figure 5: Global reach centrality (GR) of villages in (**a**) 1964; (**b**) 1996; (**c**) 2008.  
Figure 6: Global betweenness centrality (GB) of villages in (**a**) 1964, (**b**) 1996, and (**c**) 2008.  
Figure 7: Global closeness centrality (GC) of villages in (**a**) 1964, (**b**) 1996, and (**c**) 2008.  
Figure 9 shows the results for global straightness (GS), indicating the ratio of Euclidean distance to network distance between a village and all accessible villages. The smaller the value, the more physically rugged the roads. The value did not show significant changes across the studied years. However, the spatial distribution reveals that villages close to the water usually have complicated access roads. The roads of villages in the southwest area, far from the water, are nearly straight lines.