## 2 Research Subject and Methodology
### Research Methodology
#### 2.2.3 Complex Network Analysis  
The mechanism behind the network of 'nodes' and 'lines' can be understood and transcribed systematically through the complex network analysis [27], while the structural indicator system can be used to quantify and evaluate the spatial network of roads in the historic urban area. This study based its analysis of the road network's structural layout, spatial vulnerability, spatial stability, spatial balance, and accessibility to the historic area on an analysis of the road space network structure. We largely relied on quantified results to identify the features of road transport space evolution in the historic urban area and their internal driving forces to provide solutions for the improvement of the conservation and utilization of historical sites. 1. Building the Semantic Model  
The complex network method was employed to determine the 'node' element of the road (between two intersections) and the 'line' element (direct connection between adjacent intersections), which means if a road (node) is connected to an intersection, it is considered to have a connection relationship (line). Based on the urban road-space relations in the historic urban area, a 1-modular data matrix on the road-to-road relationship was  
Figure 1: Research Scope. Figure 2: Maps of Various Periods. established. This was introduced to _Ucinet_, a network analysis software program, to produce the 1-modular network matrix on the road-to-road relationship. Establishing the Model  
Software, such as _cad_ and _gis_, were used to digitalize the selected maps according to the syntactic model building principles (Figure 3). This resulted in a 1-modular relations matrix on the road-to-road relationship. The matrix was then processed by _Unicet_ to produce the 1-modular network matrix on the road-to-road relationship, which was also processed for visualization. Indicator System  
Node density refers to the degree of connection between individual nodes in the overall network. It is calculated as the ratio of the existing relations of a single individual node in the network to the total number of nodes in the network. The lower the density value is, the higher the level of vulnerability in the network. The formula is as follows:  
\[D=m/[n(n-1)] \tag{1}\]  
In Formula (1), \(D\) is the network density, \(m\) is the number of relations existing in the network with connections to the node in question, and \(n\) is the total number of nodes in the network, i.e., the scale of the network. If a point of contact is removed, the network will break down into a couple of separate parts. Therefore, it is widely accepted that the ratio of these nodes to the total number of nodes in the network can be used to access the level of vulnerability in the network. Figure 3: Network Numbering of City Roads in Various Periods. (c) Network Density  
The network density represents how closely the nodes are connected to each other in a network. Its definition is the ratio of the connections a node actually owns to the maximum number of lines it may own. The network density can be used to evaluate the degree of network completeness. The formula used is as follows:  
\[P=L/[n(n-1)/2] \tag{2}\]  
In Formula (2), \(P\) is the network density; \(L\) is the number of connections that actually exists in the network; and \(n\) is the number of nodes that actually exists in the network. (d) Lambda Collection:  
The overall stability of the network structure was measured by analyzing the edge correlation degree of the network hierarchy. (e) \(k\)-core  
\(k\)-core (\(k=1,2,3\dots\) ) was used to calculate the local stability of a measurable network, where the larger the \(k\) value, the more local network components with stable structures were contained in the network and the higher the overall network stability level. In other words, the network stability is positively correlated with the \(k\) value and the \(k\)-core ratio.