1. Network density

Network density is the ratio of the network's actual number of connected relationships to its theoretical maximum. It is applied to measure the overall structural density of the network. As well as the degree of association between network components. It is calculated as follows.

$$P = \mathcal{L} / \left[ \mathbf{n} \left( \mathbf{n} - 1 \right) / 2 \right] \tag{4}$$

P is the network density, L is the number of connections, and n is the number of nodes in the network.

2. K-core

The "K-core" is used to analyse the stability of the network's internal structure. Any point in the K-core network structure is adjacent to at least K nodes. The more stable the network topology is, the higher the K-value and the more influential the proportion of K-core.

3. Cut point

It refers to some nodes in a network. If removed, the whole network will be multiple unrelated parts. However, the network's vulnerability can appear by the number and proportion of cut points.

#### 4. Degree centrality potential

The degree centrality potential is used to analyse the centrality of the network. Describe the overall tendency of nodes to congregate at a specific point in the network, and also quantify the network structure's degree of general equilibrium. The calculation formula is as follows.

$$\mathbf{C} = \frac{\sum\_{i=1}^{n} (\mathbf{C}\_{\text{max}} - \mathbf{C}\_{i})}{\max \left[ \sum\_{i=1}^{n} (\mathbf{C}\_{\text{max}} - \mathbf{C}\_{i}) \right]} \tag{5}$$

Cmax is the maximum value of the degree centrality of each node in the network and Ci is the centrality of node i.

#### 5. Intermediary centrality

The network's intermediary nodes are those in the shortest path between other nodes. Intermediary centrality, computed as follows, increases as nodes occur in linked courses.

$$\mathbf{C\_{RBi}} = \frac{\sum\_{\mathbf{j}}^{\mathbf{n}} \sum\_{\mathbf{k}}^{\mathbf{n}} \frac{\mathbf{g\_{jk}}(\mathbf{i})}{\mathbf{g\_{jk}}}}{\mathbf{n^2} - 3\mathbf{n} + 2} \tag{6}$$

CRBi is the relative intermediate centrality of nodes, gjk(i) is the number of paths that exist between node j and node k that pass through the third point i, gjk(i) is the number of ways that exist between node j and node k, and n is the total number of nodes.

#### 6. Intermediary centrality potential

It looks at how evenly the intermediary centrality of all the nodes in the network is spread out. The formula for figuring out how to measure this is as follows.

$$\mathbf{C}\_{\rm B} = \frac{\sum\_{i=1}^{n} (\mathbf{C}\_{\rm RBmax} - \mathbf{C}\_{\rm RBi})}{n - 1} \tag{7}$$

CB is the intermediary centrality potential of the network, CRBmax is the maximum possible value of the intermediary centrality of a node, CRBi is the actual value of the intermediary centrality of node i, and n is the number of nodes in the network.

#### **3. Results**

#### *3.1. Cultural Connotation of Auspicious Elements*

3.1.1. Expression of Auspicious Culture

We did a study and analysis in the area. The results showed us how Shaxi ancient town's Bai architecture symbolises luck. It takes the building components as the expression carrier. The pursuit of auspicious symbolism is expressed through decorative elements with auspicious meaning. Extensive woodwork, small woodwork, tilework, and colour painting are the principal expression carriers. In addition, there are stone carvings, column bases, and ridge decorations. (See Figure 2).

**Figure 2.** Pictures of auspicious elements.

3.1.2. Local Expression of Auspicious Elements in Bai Traditional Architecture

Table 1 shows that the Shaxi Bai people have fully absorbed and borrowed foreign culture. They were then forming a rich combination of auspicious factors. This is a local interpretation of Shaxi Bai's fortunate foreign architecture. Furthermore, it symbolises the lucky culture of traditional Shaxi Bai architecture. It is a fusion and development of multiple cultures and local Bai culture. It shows how accepting the Bai people are of other cultures. At the same time, it shows the inheritance of their own culture.

**Table 1.** The cultural connotation of auspicious elements [25,26].



**Table 1.** *Cont.*


**Table 1.** *Cont.*
