## 3 Research Framework and Methodology
### Analysis of Cluster Identification Results with Bipartite Network  
Various clusters are obtained through MDBSCAN and DBI. To further analyze the relationship between clusters and technological topics, a bipartite network is introduced to represent their relationship. Unlike an ordinary network, a bipartite network can be compatible with nodes of both natures, while there is no association between nodes of the same type. Moreover, a bipartite network exhibits interconnected edges solely between nodes of distinct types, where the strength of the association between a pair of nodes is denoted by the weight of the connected edge [74]. The characteristic form of a bipartite network is shown in Figure 3.  
The existence of a weighted technology-applicant bipartite network \(G\) = (\(C\), \(T\), \(E\)) is assumed, where \(C\) = {\(c_{1}\), \(c_{2}\),..., \(c_{C}\)} represents the cluster set, \(T\) = {\(t_{1}\), \(t_{2}\),..., \(t_{T}\)} represents the technology topics set, and \(E\) \(\in\) (\(C\times T\)) is the edge set of \(G\). The weights are calculated as follows:  
\[e_{ij}=\left\{ \begin{array}{l}pn_{ij},e\in(c_{i}\times t_{j})\\ 0\quad,e\
otin(c_{i}\times t_{j})\end{array} \right. \tag{7}\]  
where \(pn_{ij}\) denotes the number of patents involving both the cluster \(c_{i}\) and technology \(t_{j}\). The clustering capabilities of MDPSCAN encompass both geographical and technological aspects; however, the resulting clusters can only be represented on a two-dimensional map, leaving the relationship between clusters and different technologies undisclosed. In order to improve the visualization of the cluster and technology network model, a network layout configuration is required. Specifically, a force-guided layout approach is employed for the cluster-technology relationship network, wherein the merging of nodes within clusters aims to reduce the total number of network nodes. This layout method employs the concept of spring force to calculate pairwise forces between nodes, thus centering the important nodes within the network. Consequently, this arrangement allows for a more visually coherent display of the significant clusters [75]. Based on this, different clusters are divided with Core-Periphery Network (CPN) structure facilitation. Within  
Figure 3: Bipartite network. the CPN framework, the core denotes a set of nodes located in the center and tightly intricately connected, whereas the periphery refers to a set of nodes encircling the center and loosely connected to the core. With regard to the IIC, the utilization of CPN enables the precise analysis of the technology distribution of the target cluster and its position within the overall cluster. In addition to the technology distribution, the cluster development model can also be analyzed. According to [PERSON] [76], the current cluster development models encompass four main types, namely, Italian-style industrial clusters, satellite-based industrial clusters, axle-wheel industrial clusters, and national power-dependent industrial clusters. Italian-style clusters are dominated by SMEs, exhibiting strong specialization without leading enterprises. Satellite clusters are also dominated by SMEs; however, their existence relies mainly on enterprises affiliated with other clusters. Axis-wheel-type clusters are mostly dominated by both large-scale local enterprises and SMEs, exhibiting a distinct hierarchical structure. State power-dependent industrial clusters, also referred to as government-led industrial clusters, materialize as a result of the state's support via industrial policies. Based on the definitions of the four patterns, this paper utilizes a patent analysis method to identify cluster patterns. The patent applicants encompass various entities, including enterprises, universities, and research institutes. Notably, universities and research institutes often serve as state-owned institutions in numerous countries, such as China.