## 2 Literature Review
### Traffic Dynamics from a Low-Order Perspective  
Academics have developed significant numbers of mathematical tools and computer algorithms to identify the effective approaches to detect community structures. However, most of them focused on the low-order connection patterns of individual nodes and edges. For example, the traditional technique revealed the underlying community structure by removing edges, based on the shortest path, betweenness, or successive neighborhoods [13; 14; 15]. Others tried to overcome the limitations of the conventional ones and proposed new methods, such as the degree-based core-vertex algorithm and local community neighborhood ratio function [7; 18]. Precisely, [PERSON] et al. identified the multi-community structure of the global airport network, supporting the anomalous values of centrality [3]. They insisted that the community structure cannot be explained exclusively with geographical factors. [PERSON] et al. pointed out the spatial pattern of the airport network modular structure over time in the United States [27]. However, those structures were not characterized by geographical constraints, which is consistent with [PERSON] et al. [3]. [PERSON] et al. applied hierarchical cluster analysis to compare the community configurations between high-speed rail and airline networks [4]. Similarly, the four subgroups identified in the dendrogram for airlines cannot be explained with geographical factors like the clusters that were observed in the high-speed rail network. Additionally, no clear pattern \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Categories** & **Reference** & **Year** & **Approaches** & **Sketches** \\ \hline \multirow{6}{*}{[16]} & \multirow{2}{*}{2013} & \multirow{2}{*}{2014} & Extended modularity Based on & \multirow{2}{*}{\begin{tabular}{} \end{tabular} } & Detected overlapping communities \\  & & & absorbing degree (EM-BOAD) & in weighted complex networks \\  & & & algorithm & \\  & [17] & 2014 & Enhanced NMF-based Method by & \multirow{2}{*}{\begin{tabular}{} \end{tabular} } & \multirow{2}{*}{\begin{tabular}{} \end{tabular} } \\  & & & neighborhood ratio matrix & & \\  & [18] & 2015 & Based on local community & \multirow{2}{*}{\
\begin{tabular}{} \end{tabular} } & Detected overlapping communities \\  & & & neighborhood ratio function & & \\  & [19] & 2017 & Map-Reduce approach & & \\  & & & & large-scale network \\  & & & & evaluated the result of network \\  & & & hierarchical cluster Analysis based & partitioning by calculating the & \\  & & on the modularity proposed by & difference between the number of & \\  & & Newman and Girvan [14] & edges within communities and the & \\  & [20] & 2019 & Clauset–Newman–Moore & Added a traffic-driven indicator for & \\  & & modularity maximization algorithm & weighted network & \\ \hline \multirow{6}{*}{[21]} & \multirow{2}{*}{2014} & \multirow{2}{*}{2014} & BASH (based on maximal & \multirow{2}{*}{
\begin{tabular}{} \end{tabular} } \\  & & & sub-graphs) algorithm & \\  & & ACC algorithm (based on the & \\  & & clustering coefficient of two & & \\  & & neighboring maximal sub-graphs) & \\  & & & Based on the deep and bread & \\  & & & searching for extracting all the & \\  & & & maximal cliques & \\  & & & & networks \\ High-order community & & & & \\ detection & [24] & 2017 & Infomap-based algorithm & & regularities in the flows for sparse \\  & & & & memory networks \\  & & & & & \\  & [11] & 2018 & Graph partitioning method based on & \\  & & Clique conductance minimization & & algorithm that approximately solves \\  & & & the optimization problem \\  & [25] & 2019 & Multi-layer motif (M-Motif) & Detected higher-order multi-layer \\  & & approach & & communities \\  & & An attribute-based multi-layer & & \\
[26] & 2019 & network community detection & & \\  & & algorithm (M-ALCD) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: \(Cont.\)of links between the cities' demographic information and clusters was found in the airline networks. [PERSON] et al.