Empirical Research On China Aviation Network Based On Null Model Method

Aviation network is a huge complex system,and complex network theory is an important means to study complex systems.Empirical analysis of the non-trivial nature of the existence of aviation network and its generation mechanism is of great significance to resource allocation,route planning and design,and production scheduling.In traditional empirical network research,researchers generally describe the properties of complex networks by calculating statistical indicators of complex networks.Compared with traditional empirical network research,the reference null model method provides a unified network scientific research paradigm.Based on China's flight data in 2021,this paper constructs an undirected unweighted aviation network,an undirected weighted aviation network,and a temporal aviation network,and uses the null-model algorithm to construct a null-model network of the corresponding aviation network,respectively for its actual aviation network and corresponding aviation network.The correlation properties of null-model networks are empirically analyzed.The main analysis results are as follows:(1)Construction of actual aviation network and null model networkReferring to the null-order null model construction algorithm,it is found that the degree distribution of China's aviation network is a double power-law distribution,which is a small-world network with scale-free characteristics;the larger clustering coefficient is a unique property of China's aviation network,not due to randomness.network;small average path lengths are not unique to Chinese aviation networks.Referring to the first-order null model construction algorithm,it is found that the Chinese aviation network has obvious heterogeneity.Through the simple connection guaranteed randomization(R-S)and the multiple connection guaranteed randomization(R-M)algorithm,it is found that the heterogeneity observed in the actual aviation network is a structural heterogeneity,which is caused by structural truncation and originates from the actual aviation network.The scale-free properties of the network can be fully explained by the degree distribution.A quantitative analysis of the actual aviation network is carried out using the R-value and Z-value correlation profiles,and it is found that the heterogeneity of the actual aviation network is promoted.(2)Property analysis of undirected and unauthorized aviation network with reference to null modelReferring to the null-order null model construction algorithm,it is found that the degree distribution of China's aviation network is a double power-law distribution,which is a small-world network with scale-free characteristics;the larger clustering coefficient is a unique property of China's aviation network,not due to randomness.network;small average path lengths are not unique to Chinese aviation networks.Referring to the first-order null model construction algorithm,it is found that the Chinese aviation network has obvious heterogeneity.Through the simple connection guaranteed randomization(R-S)and the multiple connection guaranteed randomization(R-M)algorithm,it is found that the heterogeneity observed in the actual aviation network is a structural heterogeneity,which is caused by structural truncation and originates from the actual aviation network.The scale-free properties of the network can be fully explained by the degree distribution.A quantitative analysis of the actual aviation network is carried out using the R-value and Z-value correlation profiles,and it is found that the heterogeneity of the actual aviation network is promoted.(3)Undirected weighted aviation network property analysis with reference to the null modelReferring to the weight random scrambling null model algorithm,it is found that the relationship between the node strength S and the node degree k of the undirected weighted network can be fitted by a linear function,and the weight distribution has a strong difference.Using the weight random scrambling algorithm,it is found that the edge weight and the network topology have no correlation.Referring to the first-order random broken edge reconnection null model,the structure random scrambled null model and the weighted random scrambled null model algorithm,by calculating the weighted matching coefficient of the weighted aviation network,it is found that the undirected weighted aviation network is heterogeneous.The weighted matching coefficient values of the weighted aviation network and the first-order random broken edge reconnection null model and the structural random scrambled null model are not much different,while the weighted matching coefficient based on the weighted random scrambled null model is about 4.5 times that of the actual weighted network.,it is found that the reason for the mismatch of the matching characteristics of the undirected weighted aviation network is the connection weight of the network,which has nothing to do with the topology of the network.Based on the weighted random null model algorithm,it is found that the weights of the routes owned by the airport nodes in the Chinese aviation network are quite different,and the edge weights in the original network show a negative correlation relative to the weight random null null model.(4)Property analysis of temporal aviation network null ModelReferring to the time-weighted scrambled null model,isochronous weighted scrambled scrambled model,contact scrambled scrambled model,and first-order connected edge scrambled scrambled model,a new time-weighted scrambled scrambled model with time-sharing is proposed.By exploring the average degree,clustering coefficient and average shortest path length of China's aviation network with the weekly mode as the time slice,it is found that the most obvious scrambling factor affecting the average degree of the original time slice network is the weight on one side of the network and the sum of all events.time probability distribution.The topological structure of the network has the greatest influence on the clustering coefficient of the original time slice network.The scrambling factor of the time-weighted scrambling algorithm considering time-sharing is the weight topology correlation of the network and the correlation between the events on the adjacent edges,which can affect the original time-slice network.While maintaining the clustering coefficient of the time slice network,it maintains the same increase as the original time slice network clustering coefficient.The most obvious scrambling factors affecting the average shortest path length of the original time slice network are the network topology and the sequence of network events.