## 3 Methodology
### Dataset  
To verify the effectiveness of the proposed method, this study conducts a comparative analysis with the top ten airline groups by passengers carried in 2019, including American Airlines Group, Delta Air Lines, Southwest Airlines, United Airlines, Ryanair, China Southern Airlines, Lufthansa Group, China Eastern Airlines, International Airlines Group (IAG) and Air China Group.  
Intersect holdings have gained increasing attention and popularity among airlines. Instead of merging several holding airlines into one, some groups prefer to maintain airlines' brands and liveries and operate as their subsidiaries. Therefore, the biggest airline is selected from each group to enable knowledge discovery and pattern detection. For  
Figure 1: Research methodology flow chart.  
example, the scheduled flights of British Airways will be analyzed on behalf of the complex network of IAG.  
Among selected airlines, Southwest Airlines and Ryanair (including Ryanair Sun) are low-cost carriers operating point-to-point networks by themselves, whereas the rest are full-service ones operating hub-and-spoke networks with their codeshare partners. Hence, they will be investigated respectively to explore the highly interconnected parts and give particular insights in terms of the topological differences between business models.  
As discussed in Section 2.2, the codeshare agreement benefits an airline considerably. It allows the airline to publish and market flights operated by partners under its flight number as part of the published timetable. Those agreements dramatically influence the airline network configuration and reshape the market dynamics worldwide [35]. Yet, most of the research considers the transportation network as an isolated system [36]. Other academics tried to tackle this issue from a multi-layer perspective. By corresponding each layer to a different airline, [PERSON] and [PERSON] calculated topological parameters for Chinese airlines and conducted a comparative analysis among them [26]. Similarly, [PERSON] et al. unveiled the multi-layer structure in the aviation industry with a special focus on communities bigger than ten nodes [37]. Likewise, [PERSON] et al. sketched the structural properties of the air transport system in Europe [29]. They noticed that the topological properties of the airline network have resulted from multi-layer characters rather than single layers. Although they compared the networks of major airlines and low-cost ones, they only took operating carriers into account, which left the codeshare system remaining almost unexplored. Therefore, it is necessary to devote efforts to and explore the way in which codeshare partners are reshaping topological properties in the aggregate network.  
A weekly scheduled non-stop flight dataset (from 1 August 2019 to 7 August 2019) is obtained from OAG (OAG is a global travel data provider with headquarters in the UK. It provides flight information data, including schedules, flight status, connection times and industry reference codes, such as airport codes), including origin, destination, operating and codeshare carriers of each flight. Because the actual passenger number is not available via multiple sources, this research weights each flight by the weekly frequency for the selected airlines accordingly. Hence, the relationships between airports are defined by both topological structures and a traffic-driven indicator. Last, but not least, this study will be primarily focused on airport level rather than city level in order to identify the key players in a multi-airport system. Hence, each airport represents a vertex, while each direct flight connecting an airport pair serves as an edge.