3.4.2. Network Local Stability

Figure 4 shows that each type of building in the old town is made up of a group of lucky elements with stable structures and close links. They reflect the parts that have a particular way of being put together to show the lucky culture. Each building type forms a unit cluster family with different cultural meanings. It suggests that the old town's lucky culture comes from a blend of cultures.

**Figure 4.** K-core diagram of auspicious elements for each building type. (**a**) is Xingjiao Temple, (**b**) is the Patron God Monastery, (**c**) is the ancient theater, (**d**) is the essential protected dwellings, (**e**) is the generally protected dwellings, (**f**) is Stores.

#### 3.4.3. Network Vulnerability

Table 4 shows the number of cut points of all architectural types of auspicious elements below 3. The co-occurrence network of lucky architectural elements is relatively safe. Moreover, all of them have formed a stable network structure. In addition, F1 (lotus flower) is the most frequent auspicious element in each building type. It reflects the more significant Buddhist impact on historic town auspicious constructions.

**Table 4.** Co-occurrence network cut points of auspicious elements by building type.


3.4.4. Intermediary Centrality

Figure 5 indicates that every building has lucky parts with high intermediate centrality. They are at the heart of the building types' fortunate elements. Each historic town building has a primary and secondary auspicious aspect. Individually, each building type almost always contains the lucky element F1 (lotus). Moreover, it has high intermediate centrality values. The lotus is vital to the ancient town's auspicious architecture. Furthermore, it also reflects Buddhism's relevance in Shaxi's old town's fortunate architecture.

**Figure 5.** Scatterplot of intermediary centrality in descending order.

#### 3.4.5. Degree Centre Potential

Figure 6 shows that the degree centrality potential of EPD (55.73%) is significantly higher than the other five building types. It indicates other building types' poorer integrity. However, the network degree centrality of EPD is apparent. It reflects that foreign cultures and better protected with less impact. In addition, most of EPD are residences of historically famous families. The owners have good economic ability and a high cultural level. It leads to the owners having significant autonomy in selecting auspicious elements. Therefore, there is a prominent theme in expressing auspicious culture in EPD. Moreover, the degree centrality potential of Xingjiao Temple (28.67%) is at the lowest level. It indicates that its network centrality is poor and its balance is high.

**Figure 6.** Bar chart of degree centre potential.
