## 5 Findings and Discussion, Contribution, Limitations and Future Work of The Study  
### Findings and Discussion  
The research aims to assess the underlying patterns in the high-order communities, and extracts the backbone of the airline network structure with a weighted clique percolation method. Ten airlines are selected from the top ten airline groups worldwide, to exemplify a comparative analysis and verify the effectiveness of the proposed method.  
Firstly, this study summarizes the patterns of major airline networks with statistical values, which illustrate the variations in the average degree and density of the selected airline networks. This paper spots the proportionate change in nodes and edges, which may result in the uncertainty of density.  
Then, the weighted clique percolation method is introduced to analyze the high-order interaction and clustering properties. Typically, most of the codeshare networks are consist in three high-order communities, whereas low-cost airlines seldom have any high-order community, due to their network structure and lack of partnerships. Meanwhile, the community configuration of BA is close to what WN has, with several key airports in each group. Regardless of the business model and network size, the similarity in high-order community structures suggests the possibility of them sharing an identical topology profile, which is the opposite of what previous studies in low-order communities have found [20]. Moreover, the communities detected by this method are separated based on geographical information, which has not been achieved by other techniques. Basically, the geographical location of the partners' network results in the geographical separation of clique communities.  
The influential nodes in the overlapping area help airlines to recognize airports' roles in the network and control the network dynamics. However, the results seem to be rather controversial. This study observes a wide hub-shifting phenomenon among six legacy airlines. The shifting can be classified into three types. The first type combines some of the airline's hubs with their partners', such as AA and BA. The result proves the complementary advantages brought by partners. In contrast, no partners' hub outside China was found in CA's network. Particularly, the outperformance of PVG establishes the international market power of Shanghai, and CA should pay attention to the emerging multi-airport configurations in China. Finally, only partners' hubs were identified in the network of CZ, DL, and UA, which may ring the bell of airlines losing dominant positions in the codeshare network. Aside from shifting, the concentration in FRA and PVG proves their hubs' strategic positions by outperforming other hub airports in the system. In MU's four-clique communities, it is also noticeable that the influential nodes extend to CDG, PVG, SIN, and SYD, offering worldwide connections, contributed to by codeshare partnerships.  
There has been very limited research targeting high-order communities in the airline network. Hence, it is not easy to conduct a comparative analysis among the published results from the limited available research. However, it is noticeable that some of the findings are consistent with the patterns that the previous literature has detected in the low-order structures. For instance, this paper identifies two medium-sized airports as gateway airports, which confirms the arguments of [PERSON] et al. and [PERSON] [3; 32].