## 1 Introduction  
Topology describes properties of space that are preserved under continuous deformations, while network topology explores the way components arrange and connect within a system [1]. With the tremendous growth of the complex networks theory and application, the air transport network has gradually formed as a complex system of flights, which considers airports and direct flights as vertices and edges [2].  
Vertices or nodes with network-specific roles emphasize the determinants of the network topology and performance [3]. In a complex network, communities usually represent the multiple subgroups or clusters, which consist of groups of vertices that locally, densely interconnect, but sparsely connect to other groups [4, 5]. In other words, nodes more heavily connect within the community, rather than across communities [6]. For instance, a community in the transportation industry may exist as several cities, which are frequently connected by bus, train, or flights. Further, communities may have features including motifs and cliques, where nodes are divided based on their qualities or their relationships with other nodes [7]. Subsequently, the existence of communities evidences the hierarchy among the interactions and features within the network.  
While the core nodes and communities act as a pivotal part in the system, community detection facilitates the uncovering of hidden relationships, revealing the interconnections and inter-dependencies among multiple parts of the complex aviation network [8, 9]. In this sense, community detection is of great value in classifying the functions of nodes and analyzing complex systems at the mesoscopic level, which cannot be easily assessed by distance measures [10; 11].  
This research aims to explore the way in which flights influence airline networks topologically, with a weighted clique-based community detection method. The principle aggregated frameworks that deem this research to be novel and unique are listed below in bullet point format:  
* This paper examines the applicability and the robustness of the weighted clique percolation method in the commercial world, with a sample of ten major airlines with different business models.
* This paper expands the research scope by taking both codeshare agreements and the flight weights into account.
* New insights in air transport geographical and topological patterns include the following: 1. The detected high-order communities can be interpreted purely based on geographical information. 2. The wide-spread topological hub-shifting phenomenon is observed, resulting in inconsistency between topological gateway airports and the actual airline hubs. 3. It is possible that airlines with the different business models and network sizes share an identical topology profile.  
This paper is structured by first reviewing the fundamental concepts of network science and community detection methods (Sections 1 and 2). Section 3 briefly explains the computational tool implemented and the sources of data in this research. They are followed by a network analysis of ten selected airlines, with a special focus on identifying and examining the community configuration and influential shared nodes (Section 4). The results are then interpreted and explained from a transport geographical point of view, to obtain an in-depth understanding of the network dynamics and airports' roles. Section 5 discusses the findings and results, emphasizing the new insights, and Section 6 concludes this paper.