Yiqio WANG ,Xinin CAO,* ,Fngyun QIN ,Lu (Crol) TONG

a School of Electronic and Information Engineering,Beihang University,Beijing 100191,China

b School of Information Engineering,Capital Normal University,Beijing 100191,China

KEYWORDS Air transportation;Complex networks;Railway network;Transfer;Vulnerability

Abstract The integrated aviation and High-Speed Railway (HSR) transportation system plays a vital role for today’s inter-city transportation services.However,an increasing number of unexpected disruptions(such as operation failures,natural disasters,or intentional attacks)pose a considerable threat to the normal operation of the system,especially on ground transfer,leading to the extensive research on its vulnerability.Previous approaches mainly focus on interruptions within a single transportation mode,neglecting the role of ground transfer which serves as a coupled connection between aviation and High-Speed Railway.This paper proposes a network-based framework for evaluating the vulnerability of the Chinese Coupled Aviation and High-Speed Railway(CAHSR) network from the viewpoint of ground transfer interruption.Taking the end-to-end travel time and passenger flow information into consideration as an evaluation measure and analyzing from the perspective of urban agglomerations,an adaptive method is developed to identify the critical cities and further investigate their failure impacts on the geographic distribution of vulnerability.In addition,the proposed model explores variations of vulnerability under different failure time intervals.Based on the empirical study,some major conclusions are highlighted as follows:(A)Only a few cities show significant impacts on the network’s vulnerability when ground transfer interruptions occurred.(B)The distribution of vulnerability is not proportional to the distance between failure city and influenced city.(C)The vulnerability is more serious in the morning and evening when the ground transfer is disconnected.Our findings may provide new insights for maintenance and optimization of the CAHSR network and other real-world transportation networks.

1.Introduction

The aviation and HSR systems in China have undergone remarkable growth over the past decade,with the world’s second largest air transportation volume and largest high-speed railway mileage,respectively.1–3As main components of inter-region transportation,aviation and HSR systems have been transformed into an integrated system which has drastically improved connectivity and brought tremendous benefits to human lives and economics.4,5In general,a well-designed aviation and HSR integrated system is expected to achieve seamless connections to eliminate travel time at transfer cities and offer more travel choices for inter-city passengers.

In recent years,transportation systems are facing increasing disruptions.Due to their importance,any unexpected failure may seriously affect public stability and economic growth.Ground transfers are the bond between aviation and HSR.The failure of ground transfer will stop passengers from transferring between different airports and/or HSR stations,leading to a non-negligible impact on the integrated system.Operation failures,traffic congestion,natural disasters,or intentional attacks all can cause the ground routes temporarily interrupted,leading to serious travel delays,forced detours,and even a huge amount of economic damage.6–9For instance,because of the ‘‘7.20” torrential storms that took place in Beijing in 2016,multiple lines of buses and subways were out of operation and few alternate routes were available,resulting in serious ground traffic confusion throughout the city and causing enormous losses.

It is therefore of great importance to model and analyze the vulnerability of transportation systems defined as the extent to which a system’s performance deteriorates when faced with disruptions.10–12In the past few decades,complex network theory has been widely used in analyzing the vulnerability of transportation systems,especially in aviation networks,13–18railway networks19,20and road networks.21,22Li and Xu analyzed the vulnerability of airport networks from a structural and functional perspective.23Ouyang et al.proposed three spatially localized failure induced models to analyze the vulnerability of the Chinese railway network.24Liu et al.used a systems-thinking approach to analyze the vulnerability of road networks.25

Although providing enlightening insights to reveal the vulnerability within the transportation system,these studies mainly focused on individual modes of transport without considering the interaction between different modes.In recent years,the coupled network has attracted great attention,26–30showing great advantages in investigating underlying relationships between interconnected modes of transportation31–33and providing a new framework for analyzing the vulnerability of the integrated transportation system.34,35Regarding the aviation and HSR coupled network,Ouyang et al.studied the vulnerability of the Chinese aviation and railway integrated system.They identified the critical nodes and edges using genetic algorithms,but only evaluated the vulnerability of single systems.36In 2019,Li et al.realized the importance of analyzing the entire vulnerability of the aviation and HSR integrated system.They located critical areas by interrupting the nodes and edges of the aviation network or HSR network and investigated the variations in vulnerability and distribution of critical areas.37These studies concentrate on interruptions taking place within the aviation and HSR networks without considering disruption on ground transfer between two modes.

To the best of our knowledge,few studies have used vulnerability analysis to investigate how integrated transportation systems are affected when ground transfers are disrupted.Hong et al.measured the vulnerability of an integrated bus and subway system by considering passengers’ preferences in intermodal transfer distance.The study found that increasing the preference of transfer distance significantly reduces the system’s vulnerability.38In our previous work,we modeled the spatially-embedded Chinese Coupled Aviation and High-Speed Railway (CAHSR) network and explored travel patterns of city pairs.An interesting finding was that the average travel time of the network is heavily affected by invalidating the ground transfer.39

Given the current need for a vulnerability analysis on ground transfer disruption,in this paper,we systemically analyze the vulnerability of the Chinese Coupled Aviation and High-Speed Railway (CAHSR) network with ground transfer disruption between different facilities (airports and/or HSR stations).We measure the topological centrality parameters of the CAHSR network based on complex network theory and also evaluate the network’s vulnerability,taking into account end-to-end travel time and passenger flow information.We identify the critical cities that should be given more protection to maintain the CAHSR network from these two perspectives.In addition,we investigate the vulnerability of the CAHSR network from the aspects of urban agglomerations,including the spatiotemporal characteristics by considering different affected geographic regions and different interruption time intervals during a day.

The rest of the paper is organized as follows.In Section 2,we describe the framework of the CAHSR network and analyze the topological centrality indicators.Section 3 defines the disruption metrics to measure the vulnerability of the CAHSR network and explores the most vulnerable cities.The vulnerability analysis of the CAHSR network in urban agglomerations is discussed in Section 4,taking into consideration geographic distribution and failure time intervals.The final conclusions are drawn in Section 5.

2.CAHSR network

2.1.Data source

We collected the domestic flight and HSR data on June 17,2016,a weekday during the summer traffic period in China.The data contains 11 087 domestic flights and 1716 HSR trains,which were obtained from the Air Traffic Management Bureau of China and China Railway Corporation,respectively.We extracted the ground transfer time between any two airports/HSR stations in the same city by Google’s Distance Matrix.40In addition,we obtained the inevitable exiting/entering time at airports/HSR stations from the literature.41The passenger flow data are obtained from Baidu migration,42which provides the percentage of total passenger flow in each city pair in the CAHSR network.After normalization,the results are allocated as the weights.

2.2.CAHSR network modeling

Based on complex network theory,the Chinese aviation and HSR integrated transportation system can be modeled as a spatially-embedded Coupled Aviation and High-Speed Railway (CAHSR)network.This is illustrated asG=｛GA,GH,C｝ in Fig.1,whereGAandGHcorrespond to the aviation network and HSR network respectively.The upper aviation networkGAcomprises 114 aviation cities(cities that only have airports)and 67 coupling cities(cities that have both airports and HSR stations),with a total of 181 nodes and 1545 edges.The lower HSR networkGHcomprises 84 HSR cities(cities that only have HSR stations)and the same 67 coupling cities,with a total of 151 nodes and 3878 edges.Crepresents all ground transfer connections within the repeated 67 coupling cities betweenGAandGH.Therefore,the CAHSR network has a total of 265 cities,and the 67 coupling cities play a significant role in connecting aviation cities and HSR cities by providing ground transfer connections.In the CAHSR network,the nodes represent major cities with aviation and/or HSR services and each of them may contain multiple airports and/or HSR stations.An edge will be built if there is at least one flight or HSR train between the two nodes.It is worth noting that if a passenger arrives at any airport or HSR station in a given city,it indicates that the passenger arrives in the city.

Fig.1 Structure of CAHSR network.

2.3.Node centrality analysis of CAHSR network

With regard to the vulnerability analysis,critical cities refer to cities that suffer more severe damage under disruptions and would cause large vulnerability.In this subsection,we measure the critical cities from the perspective of network topology based on complex network theory.43Existing studies found vulnerability is highly relevant to the topological properties of network.44,45Generally,the more important a node is in the network structure,the greater loss to the network once the node is attacked.The node centrality indicators can be used to identify the nodes that possess a high impact on the network from different perspectives.Then we use three node centrality indicators including degree centrality,betweenness centrality and closeness centrality to measure the importance of nodes in the CAHSR network.46–48

Degree centralityDrepresents a node’s importance corresponding to the total number of cities that have connecting flights and/or HSR routes to the given node.The larger the value,the more cities are directly connected to the city concerned.The degree centrality of cityican be defined as

wheredirefers to the number of cities that are directly connected with cityi,andNis the number of nodes in the network.

Betweenness centralityBrepresents the proportion of the shortest paths passing through a given node.In other words,it shows the significance of the city as a ‘‘connection bridge.”The betweenness centrality of cityiis calculated as

wheregsjis the number of the shortest paths from nodesto nodej,andis the number of shortest paths passing through nodeiingsj.

Closeness centralityCmeasures the centrality of a node based on the average length of the shortest path from the given node to all other nodes in the network.The larger the value,the smaller the average length of the shortest paths for a given node to reach other nodes.Formally,the closeness centrality of nodeiis defined as

wherelijdefines the length of the shortest path between the nodesiandj.

Table 1 shows the top 15 critical cities from the perspective of the three types of node centrality indicators in the CAHSR network.From the table,we can see that the rank of degree centrality and closeness centrality are relatively similar,with a large difference in the rank based on betweenness centrality.Cities with high degree centrality and closeness centrality all are developed provincial capitals in central China.However,these cities’ betweenness centrality is not consistently strong.For example,the mega-city Guangzhou which ranks 3rd and 4th on degree centrality and closeness centrality,respectively,lists 7th on betweenness centrality.On the contrary,cities with relatively weak degree centrality and closeness centrality may have greater betweenness centrality.The western city Xi’an ranks 13th and 12th on degree centrality and closeness centrality,respectively,but lies 2nd in terms of betweenness centrality.The other critical cities including western cities Chongqing and Chengdu,as well as tourist cities Urumqi and Kunming,have similar characteristics to Xi’an.It is worth noting that the national capital Beijing and the financial center Shanghai show leading roles on all the three centrality indicators,demonstrating their superior status in the network.The cities that were identified as critical are important in terms of network topology,so more protection should be given to guard these cities against potential disruptions.

An interesting phenomenon in Table 1 is that all cities with high centrality values are coupling cities except for aviation cities Urumqi and Kunming.This can be interpreted from a geographical point of view as shown in Fig.1.All coupling cities are located in eastern or central China,consisting of major municipalities and provincial capitals that are politically important and economically prosperous.When compared with aviation cities and HSR cities,coupling cities connect the two types of cities,leading to higher centrality values.

Table 1 Top 15 critical cities in terms of the three node centrality indicators.

3.Vulnerability of CAHSR network

We assess the vulnerability of the CAHSR network considering end-to-end travel time and passenger flow information.The end-to-end travel time is one of the foremost concerns for passengers.In addition,existing research indicated that passenger flow information has a huge influence on the vulnerability analysis of transportation networks.49The passenger flow among city pairs varies greatly,resulting in differing importance of edges within the networks.Therefore,we add the passenger flow data as the edge weight to further reveal the vulnerability of the CAHSR network.

In order to reveal the importance of aviation and HSR coupling relation,we only consider the ground transfer disruptions in the 67 coupling cities in this paper.It is worth noting that failures only occur on the ground routes.The airports and HSR stations are still functional in the city.For each city pair,we select the least time-consuming route as the measure of total travel time by Dijkstra algorithm.Besides,the passenger flow data,which represents the importance of different paths,is also taken into account.We assume that there always are empty seats on the next flight or HSR train and thus passengers can always catch on the next flight or HSR train after disruptions.

3.1.Vulnerability metrics

Based on the definition of total travel timetijfrom cityito cityj,the average total travel timetifor cityiis defined as

wheretiindicates the average total travel time from cityito all the other citiesjin the network,and the sum are taken over all theNcities in the network.Similarly,the average total travel timeunder disruption eventeis defined as

whererepresents the total travel time from cityito cityjunder disruption evente.Thus,for cityi,the average total travel time variation Δtiis defined as

In addition,the passenger flow information of each city pair is regarded as the weight of edges.With the consideration of different weight values in each sub-route,the actual impact of each route can be properly considered.Assuming passengers passkcities (including departure city and destination city) in total during travel from cityito cityj.When disruption eventeoccurs,passenger may have to detours and passkecities.Then the vulnerability from cityito cityjis defined as

wherefn（n+1）represents the weight of edge from citynto cityn+1,the vulnerabilityTof the whole network is computed as

3.2.Identification of critical cities based on vulnerability

In this subsection,we measure vulnerability by disconnecting the ground transfer in each coupling city individually.The vulnerability analysis is often used to identify the most critical cities of the transportation system.Critical cities suffer more severe damage under disruptions and would cause disproportionate consequences in those circumstances,so these cities should be given more protection in traffic management.

Fig.2 illustrates the vulnerability of the 67 coupling cities arranged from left to right in order from highest to lowest degree values.According to Fig.2,only 15 cities listed in Table 2 show significant impacts on the network vulnerability during ground transfer interruptions,called as critical cities under vulnerability analysis.When no failure event occurs,the average total travel time of the CAHSR network is 7.5036 hours and the value rises to over 7.527 hours if a critical city is interrupted.

Another phenomenon we can discern from Fig.2 and Table 2 is that ground transfer disruptions in Beijing have the highest vulnerability on the whole network,followed by Wuhan,Xi’an,Changsha,Guangzhou.Specifically,the average total travel time increased to 7.5892 hours when disruptions occurred in Beijing,indicating that all passengers will spend 5.14 more minutes.Correspondingly,the vulnerability is 1.02%,0.85%,0.72%,0.63% and 0.45% when the ground transfer in Beijing,Wuhan,Xi’an,Changsha and Guangzhou is disrupted,respectively.Except for Beijing and Guangzhou,these cities are not mega-cities and located near the center of China,lying on the intersection of multiple HSR lines running north to south.

Fig.2 Vulnerability of each coupling city following the highdegree attack strategy.

Compare to the node centrality indicators shown in Table 1,although the node centrality values of Wuhan are not high on the list,Wuhan ranks second from the view of vulnerability analysis.However,Shanghai and Shenzhen,which are megacities with high topological values,are only ranked 7th and 12th,respectively.The reason may be that these cities are located in eastern and southern China,having relatively unremarkable influences on network vulnerability performance.In conclusion,critical cities are ranked differently when they are identified using node centrality indicators as opposed to the vulnerability analysis.The nodes that are critical from the view of vulnerability analysis are not so necessary from the view of topological analysis.Most critical cities identified by vulnerability analysis are not megalopolises with high economic prospects.For traffic managers,more attention and higher priority should be paid to the critical cities to ensure the robustness of the CAHSR network.

Table 2 Vulnerability of the top 15 critical cities.

Fig.3 shows the vulnerability variations between four types of travel time when ground transfer fails in the 15 critical cities.Once the disruption occurs,passengers may have to make detours.The vulnerability of the in-flight travel timeTAand the in-HSR travel timeTHare the main factors leading to the difference in the fluctuations.For Wuhan,Xi’an,Changsha,Guangzhou,Nanjing,Taiyuan,Zhengzhou,Nanning and Shenyang,the vulnerability of the in-HSR travel timeTHis the main incremental factor as these cities are all welldeveloped in terms of the HSR industry.In case of Beijing and Shanghai,one of the main cause is the variations of the vulnerability of the in-flight travel timeTA.The result indicates that the distribution of aviation and HSR passenger flow change apparently after the disruptions.In other words,when ground transfer fails,each city absorbs the impact of disruption according to its own situation.As for the vulnerability of the waiting timeTW,it will increase significantly if the ground transfer is unavailable.It indicates that passengers need to spend more time waiting for the next flight or HSR train at the intermediate airports/HSR stations.As for the vulnerability of the transfer timeTT,it changes with the specific situation.

Fig.3 Vulnerability of four types of travel time during ground transfer failures in 15 critical cities.

4.Effects on urban agglomerations

In this section,we perform a spatiotemporal vulnerability analysis of urban agglomerations under ground transfer failures in the 15 critical cities,considering affected geographic regions and interruption time intervals.In recent years,China has adopted the concept of ‘‘urban agglomerations” and proposed various policies to focus on fostering balanced development.Each urban agglomeration consists of one (or several)hub city (or cities) and its (their) neighboring cities.50By enhancing the leadership of hub cities to promote the development of surrounding and nearby cities,the policy of urban agglomeration successfully promotes regional integration.Nowadays,urban agglomerations,as one of the vital achievements in China’s high-quality economic development,have become increasingly important both politically and economically.51,52

The development of urban agglomerations requires integrated transportation systems to be well connected.Aviation and HSR intermodal services can shrink travel time and bring small-scale cities with more benefits,which also play a critical role in connecting urban agglomerations.Therefore,it is of great significance to assess vulnerability from an urban agglomeration perspective,which can provide valuable insights about the traffic status of the urban agglomerations and point out potential development directions.53

In the CAHSR network,most of the 67 coupling cities belong to the 19 urban agglomerations proposed in the China National New-Type Urbanization Plan(2014–2020).We select the mentioned 15 critical cities and further analyze their vulnerability based on the urban agglomerations under ground transfer disruptions.It is worth noting that 13 of them are hub cities in the urban agglomerations except Hangzhou and Nanjing,which are provincial capitals in the Yangtze River Delta.The 15 critical cities mainly serve as aviation and HSR transfer facilities,connecting non-hub cities within the urban agglomeration by HSR and different urban agglomerations by aviation,which is consistent with the urban agglomeration planning.

In this section,when calculating the vulnerability metrics,we merely evaluate the travelling between urban agglomerations in the CAHSR network.Therefore,only the 173 cities within the 19 urban agglomerations are taken into consideration,including 45 aviation cities,73 HSR cities and 55 coupling cities.

4.1.Spatial vulnerability analysis

In this subsection,we measure the vulnerability in urban agglomerations during ground transfer failures of 15 critical cities with different affected geographic regions.Table 3 shows the vulnerability results of each critical city during the ground transfer disruptions.We list the regional vulnerability and the national vulnerability,which are defined as the critical city’s average impact on the cities within the urban agglomerations where the critical city is located and the average impact on the cities within all urban agglomerations,respectively.From the Table 3,we can see that the ground transfer failure of a critical city has a much greater impact on its own urban agglomeration than that on others.This phenomenon indicates that the passengers traveling from non-hub cities in an urban agglomeration heavily rely on transfers in hub cities.

Another phenomenon we can find from Table 3 is that 15 critical cities can be divided into two categories.An indicatorRis proposed to evaluate relative influence.When ground transfer failure occurs in a critical cityc,the influence indicatorRcis the ratio of regional vulnerability to national vulnerability calculated as

Table 3 Vulnerability results in different affected geographic regions during the disruption of 15 critical cities.

The difference between regional vulnerability and national vulnerability in each critical city is illustrated in Fig.4.We setR=20 as the threshold,and the 15 critical cities can be divided into the following two categories:

Fig.4 Two categories of cities.

(1) National influential cities: The cities that have a great impact on their own urban agglomerations and even on the whole country with R＜20.In order from highest to lowest national vulnerability values,these cities include Beijing,Changsha,Nanjing,Wuhan,Zhengzhou,Hangzhou and Shanghai.

(2) Regional influential cities: The cities play a dominant role in their own urban agglomerations with R＞20.In order from highest to lowest regional vulnerability values,these cities include Xi’an,Taiyuan,Nanning,Chongqing,Guangzhou,Shenzhen,Tianjin,Shenyang.

Most national influential cities are hub cities in the Jing-Jin-Ji,Yangtze River Delta,Middle Yangtze and Central Plain.The first two areas are the most prosperous urban agglomerations in China,and the last two areas are the transportation hubs of the Chinese High-Speed Railway network,located in central China.We choose Beijing as a representation of national influential cities to show the vulnerability distribution under the ground transfer failure.As shown in Table 3,when ground transfer fails in Beijing,passengers traveling from Jing-Jin-Ji have to spend 17 more minutes than normal.Moreover,Beijing also has a significant impact on other urban agglomerations,such as Ha-Chang,Central Shanxi,Shandong peninsula and even distant urban agglomerations.It is worth noting that the vulnerability is not consistent to the distance between Beijing and the affected cities.Some remote areas will be influenced more than their adjacent ones.As disrupted in Changsha,Nanjing,Wuhan,Zhengzhou,Hangzhou and Shanghai,passengers can transfer at alternative adjacent hub cities in their own urban agglomerations,leading to relatively small national vulnerability values.

For regional influential cities,the vulnerability of their own urban agglomerations is more affected than that of the others after the ground transfer fails,implying ground transfer in these cities plays a dominant role in their own urban agglomerations.Most of these cities are not the metropolis nor located in central China but have developed HSR industries and located in the north,south or west.Compared with other regional influential cities,the regional vulnerability of Xi’an is the largest,followed by Taiyuan,Nanning,Chongqing,Guangzhou,Shenzhen,Tianjin and Shenyang.The results indicate that Xi’an has a seemingly lower national vulnerability,but higher regional vulnerability,as approximately three times larger than those of Beijing.If the ground transfer of Xi’an fails,traveling from other cities in Guanzhong Urban have to spend 38.86 more minutes to get to their destinations,but only 3.6 more minutes from cities in other urban agglomerations.

4.2.Temporal vulnerability analysis

In this subsection,we evaluate the vulnerability in urban agglomerations under different disruption time intervals of 15 critical cities and identify the critical time intervals when ground transfer failure has the largest influence on network vulnerability.Previous researches have mainly concentrated on the vulnerability of the transportation network in a fixed time period.54–56However,the interruption may last for only a few hours in most cases,such as traffic control,and the disruptions may occur at any time.The frequency of flights/HSR trains fluctuates during different time intervals,so the vulnerability of the CAHSR network is easily affected by the time of disruption.To further investigate the impact of different failure time,we divide a day into 24 time intervals,i.e.,interval 1 (0:00–1:00),interval 2 (1:00–2:00),...,interval 24 (23:00–24:00) and set ground transfer failures in each interval.We select Beijing and Xi’an as the representation of national and regional vulnerability cities,respectively.The vulnerability during the ground transfer failure at 24 time intervals are shown in Fig.5,we find that the network vulnerability was changed to various extents within different disruption intervals.

Fig.5 Vulnerability results under ground transfer failures over the course of a day.

As shown in Figs.5(a) and 5(b),when the ground transfer disruption occurs in Beijing during 9:00 and 19:00,the vulnerability value is large and the fluctuations are mainly affected by the vulnerability of the waiting timeTW.Moreover,disruptions occurring from 15:00 to 17:00 have the largest influence on the CAHSR network’s vulnerability.In addition,there is a slight peak appears from 9:00 to 13:00.For the influence on Jing-Jin-Ji,the largest vulnerability time interval is between 13:00 and 18:00.In brief,for national influential cities like Beijing,the vulnerability is greatly affected if there are ground transfer disruptions from 9:00 to 18:00.

For typical regional influential city Xi’an.Figs.5(c) and 5(d) demonstrate that the vulnerability under ground transfer failure varies in different time intervals.The disruptions occurring within 8:00–11:00 and 17:00–20:00 have an obviously higher influence,and the variations are mainly affected by the increment of the vulnerability of the in-HSR travel timeTHand the waiting timeTW.As shown in Fig.5(c),the vulnerability variations in the 24 time intervals form a typical ‘‘M”shape,showing a ‘‘morning and evening peak.” The vulnerability value in most time intervals under ground transfer failure in Xi’an is smaller than that in Beijing,except 8:00–10:00 and 18:00–20:00.In addition,a similar‘‘M”shape is also observed for the vulnerability in Guanzhong Urban as depicted in Fig.5(d).However,it is worth noting that the regional vulnerability of Xi’an under ground transfer failure in 9:00–11:00 and 18:00–20:00 intervals are nearly 10 times larger and 20 times lager than that of Beijing,respectively.These results indicate that regional influential cites are extremely crucial for connecting non-hub cities within their own urban agglomerations,especially during 9:00–11:00 and 18:00–20:00 intervals.

Overall,the vulnerability value is consistently high in the daytime in national influential cities after the ground transfer disrupt.The regional influential cites tend to have a major impact on their own urban agglomeration in some time intervals,especially during 9:00–11:00 and 18:00–20:00,representing more transfer demanded need to complete during these time intervals,so more traffic protection should be provided accordingly.

5.Conclusions

In this paper,we analyze the topological centrality indicators of the CAHSR network,and use end-to-end travel time and passenger flow information to assess the vulnerability of the CAHSR network under the conditions of ground transfer disruptions.In addition,we identify the critical cities and further investigate the vulnerability of the CAHSR network from the perspective of urban agglomerations,considering different affected geographic regions and different interruption time intervals during a day.

Our analyses indicate that critical cities,based on node centrality indicators and vulnerability analyses,are not identical.Counterintuitively,only a few critical cities bear a significant impact upon the network vulnerability during ground transfer disruptions,and most of them are not megalopolises,but are located in central China.In addition,we have found that most critical cities based on vulnerability results are hub cities in the urban agglomerations.Results on the 19 urban agglomerations indicate that ground transfer in these critical cities plays an important role in the CAHSR network,but a dominant role in their own urban agglomerations.Based on the geographic distribution of vulnerability across urban agglomerations,the vulnerability distribution is not proportional to the distance between failure city and influenced city.For example,the disruption may highly affect cities in remote areas.Moreover,the influence of failure times at hourly intervals shows that the ground transfer disruptions occurring in the morning and evening will bring more serious damage,especially in the urban agglomerations where the failure cities are located.These findings may support advice for local and central government agencies to improve the CAHSR network with respect to vulnerability mitigation.It can also provide new insights for improving ground transfer conditions in future infrastructure planning for the CAHSR network.In our future research,we will focus on the optimization of the integrated transportation system and the integrated construction of aviation and High-Speed Railway infrastructure.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The first author,second author and fourth author were cosupported by the National Key Research and Development Program of China (No.2019YFF0301400) and the National Natural Science Foundation of China (Nos.61961146005,62088101).The third author was supported by Beijing Postdoctoral Research Foundation,China (No.2021-ZZ-153).