基于复杂网络理论的中国航空网络结构实证研究与分析
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摘要
随着中国经济的发展和经济全球化，航空运输业得到快速发展。从民航大国到民航强国是中国民航发展新的战略任务。航空网络是民航运输的重要资源，决定了航空运输的通达性、网络可靠性和运行效率，具有重要的经济价值和社会价值。随着民航运输规模的扩大，航空网络会变得越来越复杂，对航空运输的影响也越来越大，因此，航空网络的建设、管理是中国建设民航强国的重要战略任务和战略步骤之一。而对航空网络结构的认识和影响因素的分析，是航空网络建设管理的基础。
本文运用复杂网络理论，对2010年中国国内航空网络样本，分别从拓扑结构、枢纽层级水平和抗毁性等方面，对中国航空网络进行了结构属性的实证分析；同时运用重力模型和灰色聚类理论，分析了促使中国航空网络航线连接的经济社会因素及驱动力度。本文研究建立在真实具有大量数据的样本基础之上，其实证结果真实可靠。这些问题的研究对认识中国航空网络结构性能、了解网络结构变化的影响因素、充分开发运用航空网络功能、指导航空网络运行管理等，具有一定的理论及现实指导意义。
首先，论文分析了中国航空网络的基本统计性质以及网络的关联性。分析结果表明，中国航空网络是一个小世界网络，有着幂律下降的双段度分布曲线，网络中存在度小但是介数大的节点。纵向比较，中国航空网络在规模扩大的情况下，网络平均路径长度和簇系数在变小，表明网络结构在优化。中国航空网络以吞吐量和航距形成的节点点权和度呈现出正幂律相关性，但度值对节点吞吐量的影响大于对距离的影响；吞吐量和航距的节点点权对节点介数也均表现出正的相关性，但相关系数较小，说明机场在航空网络中的重要程度，不一定表现在吞吐量上。通过簇度相关性分析，发现当度值较大时，簇系数对度值表现出明显的幂律分布，表明中国航空网络出现了以度值较大的机场为中心的群体结构，显现出“轴辐式”的网络结构特性。
其次，采用度指标、簇系数指标、特征向量指标和介数指标，综合比较分析了中国航空网络基于枢纽功能的中心化水平。结果显示中国航空网络表现出不同水平层次的中心化：北京、上海和广州城市机场处于顶层中心，深圳、成都、昆明等一批机场形成次级中心集聚。但同时发现，作为顶层中心的三大机场，其国家中心枢纽地位不突出，三大机场中北京机场中心化功能最差，广州最好。区域枢纽功能方面，乌鲁木齐机场区域中心功能最强，其次是昆明、成都和西安；深圳和重庆机场区域中心化水平与其所处地域区位相比表现强势，如果广州机场作为国家顶层枢纽功能进一步强化，深圳机场有望成为华南地区的区域枢纽中心；重庆机场将与成都机场共同成为西南地区的区域枢纽中心。区域枢纽中心机场的中枢功能，还有较大发展容量，给未来中国航空网络的发展留下了空间。
第三，运用重力模型和灰色聚类方法，遴选出影响中国航空网络航线连接的主要经济社会因素是机场城市第三产业产值、城镇居民人均可支配收入和城镇人口数。进一步分析得出，机场城市人口与机场节点度值、旅客吞吐量这两个指标没有明显的相关性，但相比较而言，市区人口数与机场度值、旅客吞吐量的相关性要大于城市常住人口数，这或许是由中国城市行政区划范围大小不等、机场辐射范围及城市居民航空运输需求购买力等因素引起的。机场城市城镇居民人均可支配收入和第三产业产值这两者与机场旅客吞吐量和航线运量都具有较强的正相关性：可支配收入和第三产业产值越高，机场吞吐量和航线运量越大。用城市第三产业产值作为优先连接仿真的航空网络，其度分布与真实网络度分布拟合很好，而以城镇居民人均可支配收入作为优先连接的仿真网络，其度分布与真实网络度分布相差较大，说明影响中国航空网络连接的主要驱动因子体现在城市的第三产业发展水平上，而人均可支配收入，只能说明人们有这种航空运输需求的购买力，并不能代表是一种有效需求。
最后，通过网络效率、最大子集团尺寸和集群系数三大测评指标，依据度值和介数确定的机场节点重要性，进行选择攻击，计算三大指标的变化幅度，以此衡量机场节点抗击“最坏情况”破坏的能力。将中国航空网络九大重要机场节点作为选择性攻击对象，首先，分别对单个机场一次性打击后，测评数据显示，区域性枢纽机场对中国航空网络的连通性有着较大的影响，是保持中国航空网络顺畅的关键节点。其次，进行连续选择性攻击，结果显示，只需要攻击占到机场总数5%的重要机场，就能使全局网络效率下降超过50%；当被攻击节点超过22%时，网络的全局效率下降为0，说明中国航空网络在面对蓄意攻击时是异常脆弱的。按介数排序攻击比按度排序攻击对网络破坏更大，表明介数大的节点对网络连通性产生的影响比度大的节点要大。北京、广州和上海3个中心枢纽机场分别受到攻击失效后，呼和浩特、哈尔滨和贵阳承受的流量增量最大；昆明、成都、西安等区域中心遭受攻击失效后，拉萨、西宁和兰州的流量增量最大；深圳机场遭受攻击后，其流量主要通过北京、广州、上海三大机场保持网络的连通性，但对其他所有区域枢纽机场的影响强度都不是很大。
With the development of China's economy and economic globalization, air transportation has beendeveloping fast. It is a new strategic task for Chinese civil aviation to develop from a large one into apowerful one. As an important resource of civil aviation transportation, airline network determines theaccessibility of air transport, network reliability and operational efficiency and shows importanteconomic and social value. Due to the expansion of the scale of civil aviation transportation, aviationnetwork will become more and more complex, and the influence on air transport would get deeper anddeeper. Thus, the construction and management of airline network is one of the essential strategicmissions and steps to build a powerful China civil aviation. The cognition of airline network structureand the analysis of affecting factors are the foundation of airline network construction management.
With the help of the Complex Network Theory, we use the2010Chinese domestic airline networksamples to carry out an empirical study of Chinese domestic airline network structure from aspects asfollows: the topology structure, hub hierarchy level and anti-destruction ability. Meanwhile, the gravitymodel and Grey Clustering Theory are also applied to the analysis of the economic and social factorsand driving forces that influence the connection of Chinese airline network services. These studies arebased on large numbers of real data samples and therefore the empirical results are reliable. As a result,this research is of certain theoretical and practical significance for people to understand Chinesenetwork structure performance and the factors that affect the network structure change, to fully developairline network functions, and to direct the management of aviation network operation.
First of all, this essay analyzes the basic statistical characters and the connectivity of Chinese airlinenetwork. The results show that Chinese airline network is a small-world network with degreedistribution obeying a double power-law. There exist nodes with low degree but high betweenness. Inlongitudinal comparison, while the scale of Chinese airline network accelerates, the average number ofpath length and cluster coefficient gets lower, showing that the network structure is under optimization.In Chinese aviation network, the weight and degree of the node, formed by throughput and flightdistance, have power law relationship, but the effect of degree on throughput is more than that ondistance. The node’s weight of throughput and flight distance also presents a positive correlation withthe node’s betweenness, but the correlation coefficient is smaller, showing that the position of an airportin the airline network is not definitely decided by its throughput. Through the analysis of clustercoefficient correlation, we’ve found that when the degree value is high, the cluster coefficient shows an obvious power-law distribution on degree value, which indicates that Chinese airline network appearedto form the group structure whose center is the airports with large degree, and is characterized with a"Hub-and-Spoke "network structure.
Second, using the complex network-centric theory of degree centrality, clustering coefficient andeigenvector centrality as analysis tools, this paper comprehensively compares and analyzes thecentralization level of Chinese airline network based on the hub function. It turns out that China's airnetwork shows different levels of the centric: airports in Beijing, Shanghai, and Guangzhou are amongthe top centers and those in Shenzhen, Chengdu, Kunming have become the subordinate centers.Meanwhile, we’ve found that the three top-centre airports fail to make their position of top-levelprominent. Among the top three hub airports, Beijing airport turns out to be the weakest in the functionof centrality and Guangzhou airport the strongest. In terms of regional hub function, Urumchi airportshows the most powerful function and airports in Kunming, Chengdu, Xi’an follow. The centralizedlevel of regional hub airports in Shenzhen and Chongqing is outstanding, and so are the locations. IfGuangzhou airport could consolidate its function of national top-level hub, the vision that Shenzhenairport becomes the area hub in South China would be just in sight. Also, Chongqing airport andChengdu airport might be the area hub in Southwest China. There is still huge capability for the areahub airports to develop, which allows China’s airline network to achieve more developments.
Thirdly, with the help of the principles of gravity model and the grey clustering method, wedetermine the main social factors of economy which influence the connection of China’s airline network.These factors are the urban per capita disposable income out of the airport, the town population and thecity's tertiary industry output. A further analysis reveals that the population in the airport city does nothave obvious correlation with the node degree value of airport nor passenger throughput. However,comparatively, urban population is more correlated to the node degree value of airports and passengerthroughput than city permanent population is. It seems to result from factors like the various ranges ofChinese administrative divisions, airport radiation limits, urban residents’ purchasing power for airtransport demand and so on. The average DPI of urban residents in airport cities and the tertiary industryoutput value have strong positive correlation with the passenger throughput and the course volume: thehigher the former ones are, the geater the latter ones turn out. When we use the tertiary industry outputvalue as the primary factor in connecting the modeling of aviation network, its degree distribution turnsto be similar as that in a real network, which means the main driving factor that influences Chineseaviation network connection lies in the development level of the tertiary industry output value, while, asto their demand for air transport, the DPI just shows people’s purchasing power instead of an effectivedemand.
Lastly, according to the degree value and the betweenness, we can confirm the importance of theairport nodes, and after the selective attack, we can figure out the amplitude of variation of threeindexes: the network effectiveness, the size of the biggest group and the clustering coefficient, whichwould be used in estimating the airport’s anti-worst-situation ability. Choosing9important airportnodes of Chinese aviation network as the objectives of attack, we firstly make disposable attack toevery single node, and the evaluation data show that regional hub airports contribute more to theconnectivity of Chinese aviation network, which means they are the key points to maintain thesmoothness of the network; secondly, we make continuous attack, and the figures show that only if wetake down the important airports as many as5%of the total number, can we decrease the efficiency ofthe whole network by more than50%, and when the attacked nodes increase to more than22%, theefficiency would decrease to0, which in all means being faced with deliberate attack, Chineseaviation network becomes extremely fragile. Attacks sorted by betweenness do more damage to thenetwork than attacks sorted by degree value, meaning that compared with high degree value nodes,high betweenness ones bring more influence to the connectivity of the network. With the breakdownof3hub airports: Beijing, Guangzhou and Shanghai, the passenger flow of Hohhot, Harbin andGuiyang goes up; With the breakdown of regional hub airports, the passenger flow of Lhasa, Xiningand Lanzhou goes up; when Shenzhen airport is attacked, the flow mainly goes through Beijing,Guangzhou and Shanghai to keep the network connectivity, although, it has no big effect on all theother regional hub airports.
本文运用复杂网络理论，对2010年中国国内航空网络样本，分别从拓扑结构、枢纽层级水平和抗毁性等方面，对中国航空网络进行了结构属性的实证分析；同时运用重力模型和灰色聚类理论，分析了促使中国航空网络航线连接的经济社会因素及驱动力度。本文研究建立在真实具有大量数据的样本基础之上，其实证结果真实可靠。这些问题的研究对认识中国航空网络结构性能、了解网络结构变化的影响因素、充分开发运用航空网络功能、指导航空网络运行管理等，具有一定的理论及现实指导意义。
首先，论文分析了中国航空网络的基本统计性质以及网络的关联性。分析结果表明，中国航空网络是一个小世界网络，有着幂律下降的双段度分布曲线，网络中存在度小但是介数大的节点。纵向比较，中国航空网络在规模扩大的情况下，网络平均路径长度和簇系数在变小，表明网络结构在优化。中国航空网络以吞吐量和航距形成的节点点权和度呈现出正幂律相关性，但度值对节点吞吐量的影响大于对距离的影响；吞吐量和航距的节点点权对节点介数也均表现出正的相关性，但相关系数较小，说明机场在航空网络中的重要程度，不一定表现在吞吐量上。通过簇度相关性分析，发现当度值较大时，簇系数对度值表现出明显的幂律分布，表明中国航空网络出现了以度值较大的机场为中心的群体结构，显现出“轴辐式”的网络结构特性。
其次，采用度指标、簇系数指标、特征向量指标和介数指标，综合比较分析了中国航空网络基于枢纽功能的中心化水平。结果显示中国航空网络表现出不同水平层次的中心化：北京、上海和广州城市机场处于顶层中心，深圳、成都、昆明等一批机场形成次级中心集聚。但同时发现，作为顶层中心的三大机场，其国家中心枢纽地位不突出，三大机场中北京机场中心化功能最差，广州最好。区域枢纽功能方面，乌鲁木齐机场区域中心功能最强，其次是昆明、成都和西安；深圳和重庆机场区域中心化水平与其所处地域区位相比表现强势，如果广州机场作为国家顶层枢纽功能进一步强化，深圳机场有望成为华南地区的区域枢纽中心；重庆机场将与成都机场共同成为西南地区的区域枢纽中心。区域枢纽中心机场的中枢功能，还有较大发展容量，给未来中国航空网络的发展留下了空间。
第三，运用重力模型和灰色聚类方法，遴选出影响中国航空网络航线连接的主要经济社会因素是机场城市第三产业产值、城镇居民人均可支配收入和城镇人口数。进一步分析得出，机场城市人口与机场节点度值、旅客吞吐量这两个指标没有明显的相关性，但相比较而言，市区人口数与机场度值、旅客吞吐量的相关性要大于城市常住人口数，这或许是由中国城市行政区划范围大小不等、机场辐射范围及城市居民航空运输需求购买力等因素引起的。机场城市城镇居民人均可支配收入和第三产业产值这两者与机场旅客吞吐量和航线运量都具有较强的正相关性：可支配收入和第三产业产值越高，机场吞吐量和航线运量越大。用城市第三产业产值作为优先连接仿真的航空网络，其度分布与真实网络度分布拟合很好，而以城镇居民人均可支配收入作为优先连接的仿真网络，其度分布与真实网络度分布相差较大，说明影响中国航空网络连接的主要驱动因子体现在城市的第三产业发展水平上，而人均可支配收入，只能说明人们有这种航空运输需求的购买力，并不能代表是一种有效需求。
最后，通过网络效率、最大子集团尺寸和集群系数三大测评指标，依据度值和介数确定的机场节点重要性，进行选择攻击，计算三大指标的变化幅度，以此衡量机场节点抗击“最坏情况”破坏的能力。将中国航空网络九大重要机场节点作为选择性攻击对象，首先，分别对单个机场一次性打击后，测评数据显示，区域性枢纽机场对中国航空网络的连通性有着较大的影响，是保持中国航空网络顺畅的关键节点。其次，进行连续选择性攻击，结果显示，只需要攻击占到机场总数5%的重要机场，就能使全局网络效率下降超过50%；当被攻击节点超过22%时，网络的全局效率下降为0，说明中国航空网络在面对蓄意攻击时是异常脆弱的。按介数排序攻击比按度排序攻击对网络破坏更大，表明介数大的节点对网络连通性产生的影响比度大的节点要大。北京、广州和上海3个中心枢纽机场分别受到攻击失效后，呼和浩特、哈尔滨和贵阳承受的流量增量最大；昆明、成都、西安等区域中心遭受攻击失效后，拉萨、西宁和兰州的流量增量最大；深圳机场遭受攻击后，其流量主要通过北京、广州、上海三大机场保持网络的连通性，但对其他所有区域枢纽机场的影响强度都不是很大。
With the development of China's economy and economic globalization, air transportation has beendeveloping fast. It is a new strategic task for Chinese civil aviation to develop from a large one into apowerful one. As an important resource of civil aviation transportation, airline network determines theaccessibility of air transport, network reliability and operational efficiency and shows importanteconomic and social value. Due to the expansion of the scale of civil aviation transportation, aviationnetwork will become more and more complex, and the influence on air transport would get deeper anddeeper. Thus, the construction and management of airline network is one of the essential strategicmissions and steps to build a powerful China civil aviation. The cognition of airline network structureand the analysis of affecting factors are the foundation of airline network construction management.
With the help of the Complex Network Theory, we use the2010Chinese domestic airline networksamples to carry out an empirical study of Chinese domestic airline network structure from aspects asfollows: the topology structure, hub hierarchy level and anti-destruction ability. Meanwhile, the gravitymodel and Grey Clustering Theory are also applied to the analysis of the economic and social factorsand driving forces that influence the connection of Chinese airline network services. These studies arebased on large numbers of real data samples and therefore the empirical results are reliable. As a result,this research is of certain theoretical and practical significance for people to understand Chinesenetwork structure performance and the factors that affect the network structure change, to fully developairline network functions, and to direct the management of aviation network operation.
First of all, this essay analyzes the basic statistical characters and the connectivity of Chinese airlinenetwork. The results show that Chinese airline network is a small-world network with degreedistribution obeying a double power-law. There exist nodes with low degree but high betweenness. Inlongitudinal comparison, while the scale of Chinese airline network accelerates, the average number ofpath length and cluster coefficient gets lower, showing that the network structure is under optimization.In Chinese aviation network, the weight and degree of the node, formed by throughput and flightdistance, have power law relationship, but the effect of degree on throughput is more than that ondistance. The node’s weight of throughput and flight distance also presents a positive correlation withthe node’s betweenness, but the correlation coefficient is smaller, showing that the position of an airportin the airline network is not definitely decided by its throughput. Through the analysis of clustercoefficient correlation, we’ve found that when the degree value is high, the cluster coefficient shows an obvious power-law distribution on degree value, which indicates that Chinese airline network appearedto form the group structure whose center is the airports with large degree, and is characterized with a"Hub-and-Spoke "network structure.
Second, using the complex network-centric theory of degree centrality, clustering coefficient andeigenvector centrality as analysis tools, this paper comprehensively compares and analyzes thecentralization level of Chinese airline network based on the hub function. It turns out that China's airnetwork shows different levels of the centric: airports in Beijing, Shanghai, and Guangzhou are amongthe top centers and those in Shenzhen, Chengdu, Kunming have become the subordinate centers.Meanwhile, we’ve found that the three top-centre airports fail to make their position of top-levelprominent. Among the top three hub airports, Beijing airport turns out to be the weakest in the functionof centrality and Guangzhou airport the strongest. In terms of regional hub function, Urumchi airportshows the most powerful function and airports in Kunming, Chengdu, Xi’an follow. The centralizedlevel of regional hub airports in Shenzhen and Chongqing is outstanding, and so are the locations. IfGuangzhou airport could consolidate its function of national top-level hub, the vision that Shenzhenairport becomes the area hub in South China would be just in sight. Also, Chongqing airport andChengdu airport might be the area hub in Southwest China. There is still huge capability for the areahub airports to develop, which allows China’s airline network to achieve more developments.
Thirdly, with the help of the principles of gravity model and the grey clustering method, wedetermine the main social factors of economy which influence the connection of China’s airline network.These factors are the urban per capita disposable income out of the airport, the town population and thecity's tertiary industry output. A further analysis reveals that the population in the airport city does nothave obvious correlation with the node degree value of airport nor passenger throughput. However,comparatively, urban population is more correlated to the node degree value of airports and passengerthroughput than city permanent population is. It seems to result from factors like the various ranges ofChinese administrative divisions, airport radiation limits, urban residents’ purchasing power for airtransport demand and so on. The average DPI of urban residents in airport cities and the tertiary industryoutput value have strong positive correlation with the passenger throughput and the course volume: thehigher the former ones are, the geater the latter ones turn out. When we use the tertiary industry outputvalue as the primary factor in connecting the modeling of aviation network, its degree distribution turnsto be similar as that in a real network, which means the main driving factor that influences Chineseaviation network connection lies in the development level of the tertiary industry output value, while, asto their demand for air transport, the DPI just shows people’s purchasing power instead of an effectivedemand.
Lastly, according to the degree value and the betweenness, we can confirm the importance of theairport nodes, and after the selective attack, we can figure out the amplitude of variation of threeindexes: the network effectiveness, the size of the biggest group and the clustering coefficient, whichwould be used in estimating the airport’s anti-worst-situation ability. Choosing9important airportnodes of Chinese aviation network as the objectives of attack, we firstly make disposable attack toevery single node, and the evaluation data show that regional hub airports contribute more to theconnectivity of Chinese aviation network, which means they are the key points to maintain thesmoothness of the network; secondly, we make continuous attack, and the figures show that only if wetake down the important airports as many as5%of the total number, can we decrease the efficiency ofthe whole network by more than50%, and when the attacked nodes increase to more than22%, theefficiency would decrease to0, which in all means being faced with deliberate attack, Chineseaviation network becomes extremely fragile. Attacks sorted by betweenness do more damage to thenetwork than attacks sorted by degree value, meaning that compared with high degree value nodes,high betweenness ones bring more influence to the connectivity of the network. With the breakdownof3hub airports: Beijing, Guangzhou and Shanghai, the passenger flow of Hohhot, Harbin andGuiyang goes up; With the breakdown of regional hub airports, the passenger flow of Lhasa, Xiningand Lanzhou goes up; when Shenzhen airport is attacked, the flow mainly goes through Beijing,Guangzhou and Shanghai to keep the network connectivity, although, it has no big effect on all theother regional hub airports.
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