# A Study on Finding Partners through Patent Network Analysis of UAM (Urban Air Mobility)
## 2 Theoretical Background and Hypothesis
### Network Analysis
\[C_{D}(p_{k})=\sum_{i=1}^{n}a(p_{i},\ p_{k}) \tag{1}\]  
It is normalized by  
\[C_{D^{*}}(p_{k})=\frac{C_{D}(p_{k})}{n-1} \tag{2}\]  
where \(n\) is the number of nodes in the network and (\(p_{i}\), \(p_{k}\)) = 1 if and only if node \(i\) and \(k\) (i.e., \(p_{i}\) and \(p_{k}\)) are connected; (\(p_{i}\), \(p_{k}\)) = 0 otherwise. Degree centrality only plays an analysis role in the local scope, as it only considers statistics by connection relationship. The study did not consider the direction of in-degree or out-degree, but only confirmed partnerships. Closeness centrality is a statistical indicator of centrality that considers not only direct connections but also indirect connections. It indicates how close a company is to other companies in virtual space and can be expressed in \(C_{c}\) (\(P_{k}\)) as shown in Equation (3) when there are companies named \(P_{i}\) and \(P_{k}\) among \(n\) companies. In Equation (3), \(d\) (\(P_{i}\), \(P_{k}\)) is the number of shortest distances between node \(i\) and node \(k\), and \(n\) is the number of total enterprises. \[C_{C}(p_{k})=\left[\sum_{i=1}^{n}d(p_{i},\ p_{k})\right]^{-1} \tag{3}\]  
It is normalized by  
\[C_{C^{*}}(p_{k})=\frac{C_{C}(pk)}{n-1} \tag{4}\]  
The global centrality of the network can be determined by calculating the virtual distance between all nodes connected to each node. In other words, when closeness centrality increases, it is easy to access and secure influence, status, information rights, etc. in the network. Betweenness centrality is a statistical indicator of whether the node is good at acting as a broker (intermediary). \[C_{B}(p_{k})=\sum_{i<j}^{n}\frac{g_{ij}(P_{k})}{g_{ij}}\ ;i\
eq j\
eq k \tag{5}\]  
It is normalized by  
\[C_{B^{*}}(p_{k})=\frac{C_{B}(pk)}{\left[(n-1)(n-2)/2\right]} \tag{6}\]  
In Equation (5), \(g_{ij}\) is the shortest path linking pi and \(p_{j}\), and \(g_{ij}\) (\(p_{k}\)) is the geodesic distance linking \(p_{i}\) and \(p_{j}\) that contains \(p_{k}\). Betweenness centrality expresses how much a node contributes to the interconnection of other nodes, and if betweenness centrality is large, it can be interpreted as a node having high influence in the flow of communication within the network. In this study, patent analysis of 19 companies leading the eVTOL market established a total technical classification system (Tech-tree) of the eVTOL market and derived detailed technology-specific competitiveness analysis and related component companies through various patent-analysis indicators. While we cannot claim that patent indicators directly represent the R&D performance of a particular company, as patents have been used as a main indicator for measuring R&D activity in many existing studies [35], it is reasonable to say that it does indicate a certain level of R&D activity, as evidenced by quantitative empirical studies that examined the relationship between R&D activities, patents, and corporate market changes [32; 36; 37]. After analysis of prior research that patent activity and patent quality increased with sales growth and per employee sales, prior research that patent holders with high-quality patents were more successful than patent holders with low-quality patents [38], and development trends of eVTOL companies, the following hypothesis was established. * **H1. _Patent holders with high-quality patents will have higher levels of technology development than patent holders with low-quality patents._**  
Recent studies have evolved to apply more precise analytical methods using large volumes of surge information, moving away from the level of analysis and evaluation of the potential and growth of a small number or individual patents. Through this, research can provide a more credible macro view of the technology's in/out linkage structure for technological development trends [39]. Network analysis, as is used in the analysis, is a methodology suitable for identifying complex structures of interconnection between specific subjects or technologies [40; 41].