## 4 Clique Percolation Community Detection
### Airports' Roles in Codeshare Network: Hub Shifting or Hub Concentration  
In the physical airline network, the hub is usually highly connected within the country and to the hubs of other corresponding airlines [29]. This is the result of airline aggregations and alliances decisions under a series of legal, commercial, and technical considerations [38]. Further, this concept indicates the hierarchy among airports, particularly when a carrier runs a multi-hub system. Therefore, hub airports become crucial to airlines' strategic resource optimization. Topologically, the hub airport, connecting different parts of the network, usually refers to the shared node in the overlapped communities. Hence, at least two communities are necessary for the identification of the overlapping area. Meanwhile, if no shared node is identified, this indicates either the topological isolation of each community, or only one well-connected community detected in the network. In fact, this issue becomes especially vital in an aggregated codeshare network. Whether the hub of an airline can be identified as the shared node reflects the airline's strategic position in the cooperation. To be more specific, if a partner's hub is identified as the shared node, it reveals a possible hub shifting in the codeshare network. This could result from a partner with strong market power, or from the airline losing its dominant position in connecting different regions. In this sense, discovering the influential shared nodes helps airlines to not only recognize the pattern of intercommunity and intracommunity connections, but also understand its position in the network and control the network dynamics regionally. One main function of the clique percolation method is to identify the overlapping areas. The results show that the hub-shifting phenomenon has been widely observed among six full-service airlines. For instance, although LHR and LGW are BA's hubs in London, three airports (DUB, JFK, and LHR) are marked as influential among its four-clique communities. While JFK and DUB are the hub airports of AA and Aer Lingus (EI), the result proves the partners' contribution in the complex codeshare network, such as enhancing the BA's trans-Atlantic and major European market. More specifically, EI is the flag carrier and the second largest airline in Ireland, now a wholly owned subsidiary of IAG. The detection of DUB confirms the operating strategy of IAG as a group, together with the oneworld alliance partnership with AA. Similarly, only two of AA's hubs (LAX and MIA) are marked among its ten hubs in the United States. SEA is identified as the shared node, along with LAX, among three-clique communities, while GRU, LAX, and MIA are found to be influential among four-clique communities. Since SEA and GRU are the hub airports of Alaska Air Group (AS and QX) and LATAM Brasil (JJ), it can be concluded that the codeshare inside and outside the alliance provides complementary advantages for the airline network, and leads to the hub shifting. Similar results are found in CA's network. Precisely, PEK and PVG are detected in the overlapped area among the four-clique communities, whereas CA originally hubs in PEK and CTU. Unlike previous examples, PVG is not a hub airport operated by CA's partner outside China. In contrast, the outperformance of PVG establishes the international market power of Shanghai as a possibly geopolitical-based core region, connecting China to the rest of the world [39]. While constant change happens in the aviation sector, CA may encounter more hub shifting with the emerging multi-airport configurations, particularly after the operation of Beijing Daxing International Airport (PKX) and Chengdu Tianfu International Airport (TFU). The newly identified influential airports expand the airline's connectivity by providing additional transit opportunities and flights covering more regions.