## 2 Research Methodology  
The causality hypothesis can be briefly described as follows. If two variables Y and X are given at a given time interval, and if the behavior of variable Y can be predicted, including on the basis of variable X, using historical values of both X and Y, and not only historical values of Y. Transfer entropy is a method in information theory that can make it possible to assess the relationship and direction of causality due to its asymmetry. Transfer entropy can measure both the direction and the amount of information transmitted, which is suitable for nonlinear spatial and temporal modeling of cause-and-effect relationships of traffic flows.  
The research proposes a dynamic causality analysis methodology including several main stages. Firstly, transfer entropy is applied to detect the air transportation flows' causality from the given air transportation flows' time series data for the given air transportation network to calculate the transfer entropy matrix, which can denote the dynamic nonlinear causal relationships of the air transportation system's states among different regions' transportation flows. Secondly, the matrix of causal correlation coefficients used to design the transfer entropy graph of the system's interactions is calculated on the basis of the transfer entropy matrix. This obtained graph can be used for various tasks, for example, the search for maximum flow, analysis of the network connectivity, graph-based entropy determination, etc. This may allow us to identify and analyze the dynamic properties of the air transportation system, reflecting hidden socio-economic processes.  
Statistical data reflecting the quantitative characteristics of passenger and freight flows at selected time intervals were used as a source of information for analyzing the characteristics of the communication space. Statistical data were obtained from open sources (reports and databases) and are presented in the form of time series [33; 34; 35; 36; 37].  
Figure 2 shows the life cycle of the entropy transfer-based model's formation. The first stage involves collecting data from the available sources and forming the raw data. The second stage involves data processing (ETL process): removing outliers, filling gaps, and  
normalizing and preparing the dataset. The third stage involves forming the data arrays used to determine the entropy transfer values and forming an entropy transfer graph based on the data obtained.  
When analyzing time series, trends should be taken into account, including seasonal trends. For the first two examples, models were built, in which time series were represented by a small (available) dataset. The entropy transfer analysis algorithm requires more data. Therefore, averaged results were obtained for these examples. In the third case (an example for regions of the world), there are more available data, which made it possible to show the dynamics of interactions (trends).  
When formalizing the problem statement, mathematical objects are used: time series, matrices, the concept of entropy, entropy transfer, graphs, and entropy transfer graphs. Next, we consider the elements of the analysis used to construct entropy transfer graphs, on the basis of which we can draw a conclusion about the properties of the communication space under consideration.