Structural Efficiency and Robustness Evolution of the US Air Cargo Network from 1990 to 2019

. As the US air cargo network (USACN) becomes a crucial part of the economy, it is pivotal to understand the structural evolution of the network and how it would be aﬀected by unexpected events. We investigated the network structure, eﬃciency, and robustness of the USACN from 1990 to 2019 due to targeted attacks based on complex network theory from a dynamic and spatiotemporal perspective. Our results suggest that the USACN has enhanced robustness. Moreover, we ﬁnd that attacks based on betweenness centrality are the most eﬀective way to cause a collapse compared with attacks based on degree and closeness centrality. In addition, airports of the USACN have formed an increasing number of communities with geographical ties, and airports in the noncontiguous regions are more vulnerable than other communities in the lower 48 states. Further, we discover that the average path lengths have increased, and the overall eﬃciency has decreased from 0.7 to 0.4 due to the dependency of the hub-and-spoke structure. This paper complements previous studies on the dynamic structure evolution of air cargo networks through the lens of complex network theory with spatial-temporal data.


Introduction
Air transportation contributes to a large proportion of the global economy, and it has drawn increasing attention from scholars during recent years.According to [1], though the air cargo industry transports 1% of the total volume, it contributes to 35% of the total world trade value.Despite its importance, there has been a lack of literature on the resilience of air transportation networks as opposed to other types of networks such as railroad, subway, and power grid.Multiple real-world scenarios in the past have suggested that disruptions such as severe weather events, terrorist attacks, or global pandemics could bring catastrophic effects for the airline industry and regional and global economics for both air passenger and cargo networks.erefore, it is of paramount value to assess the robustness of the air transport network when facing either random errors or targeted attacks.e most recent case of the COVID-19 global pandemic has had a devastating impact on the air transportation industry and the global economy beginning from April 2020 with the travel restrictions grounding flights and blocking connections amongst cities.Both air passenger and cargo demand plummeted 69.7% and 20%, respectively, while the air cargo demand decreased slower due to the global shortage of medical supplies and equipment.Moreover, according to [1], 44 million jobs in the aviation industry were affected, in addition to a net loss of 118.5 billion USD in the air passenger sector, and 173 billion USD in the cargo sector.Consequently, it is critical to study the mechanism of air transportation network structures, efficiency, and robustness when facing similar disruptions.Graph theory and complex network theory are the main tools scholars employed to investigate the characteristics of the air transportation network [2][3][4][5].In summary, previous studies have examined topology using cross-sectional data, and therefore, there is a lack of literature in academia that explores the air transport network from a temporal perspective.
In this study, we aim to (1) explore the topological evolution of the USACN through the lens of spatialtemporal view and (2) empirically examine the spatial properties including overall network efficiency, robustness, and community structures.e rest of the paper is structured as follows.Section 2 briefly encapsulates the previous literature.Section 3 describes the methodologies.In section 4, we portray the spatial-temporal evolution of the USACN from 1990 to 2019.Section 5 describes the characteristics of robustness and efficiency.Finally, in Section 6, we conclude this study with some discussion.

Literature Review
A wide spectrum of literature has investigated the air transportation network in the past, which can be categorized into three main groups.e first group describes the topological features of the air transportation network, and the connections to the cities.Branching from this line of research, the second group of studies has also explored network robustness and accessibility for both air cargo and passenger networks.e third group of literature focuses majorly on the economic implications of the air transportation network, covering a wide spectrum of topics ranging from the concept of Aerotropolis [6] to the business model such as LCC and FSC [7], carbon emission [8], gravity model and granger causality test [9] to investigate the economic connections between airports and local and regional economics, ticket fare based on the air transportation network structure, and fuel efficiency for passenger and air cargo market.In addition to the policy in the air transportation industry, which is the fundamental driving force for the development.

Network Topography.
In the research of the topology of the network structure, scholars have extensively employed complex network theory to assess the network structure on varieties of geographical scales such as EU, US, India, Brazil, and China [10][11][12][13][14][15][16][17][18][19].Further, air passenger and cargo have been explored separately, though there is a nonproportional number of studies centered on the air passengers as opposed to cargo counterpart.One reason for such unbalance in academia is that the economic contribution of the air cargo industry has drawn increasing attention only during recent years.Most of the previous studies have identified the small-world and scale-free properties on a variety of geographical scales [20] [21].
e authors of [22,23] analyzed the world airport network and uncovered the fact that the traffic between airports is subject to the capacity of the airports, and by simulating a global epidemic outbreak, they conclude that the air transport network could accelerate the speed of transmission.e authors of [3] performed an analysis on the global air cargo transport network using flight frequency and discovered that air cargo networks have a unique structure because of their operational differences.e authors of [24] analyzed the air cargo network structures using the case of FedEx and UPS and further illustrated the differences between cargo and passenger counterparts.
Given the growing economic contribution of the air transportation network, the robustness and resilience have drawn an increasing number of investigations to assess the robustness of the air transportation network weighted [45][46][47].Geographically speaking, scholars inspected the robustness of air transportation networks in the EU [17,48], the US [46,49], and China [50,51].Dunn and Wilkinson [52] compared two strategies for increasing the resilience of air traffic networks: an adaptive reconfiguration strategy and a permanent rerouting strategy.[49,52] examined the resilience of the US national airport network based on network science and proposed that adaptively rerouting and recovery strategies would increase the robustness.e authors of [53] evaluated the network performance and revealed that airports' robustness is affected by different key factors during large-scale disruptive events.Regardless, most of the preceding studies suggest that the air transport network robustness is related to the structural formation, which is determined by political, economic incentives of airline companies, and local (regional) policies.e authors of [7] discovered that EU, China, and North American airlines began the transition from the single model to a hybrid model to increase network efficiency.

Air Transportation Liberalization Policy and Economic
Development.
e third group of literature explores the driving force for air transportation development-policy and management strategies-which has drawn a renewed interest on a variety of geological scales, with plenty of empirical evidence in multiple geographical regions, such as the US-Caribbean [54], EU [55], Africa [56], Asia [57], and the Middle East [58].All the above studies have confirmed that air transport liberalization has brought economic properties to those regions.e authors of [59] examines 184 countries and discovered that liberalization has fostered the increase of passenger flow.From a temporal perspective, [60] suggested that the long-term OECD air transportation demand depends on the level of liberalization policies.Additionally, the prevalence of the LCC (low-cost carriers) across the globe has tremendously stimulated local and regional economic growth [7,20,[61][62][63][64][65].

Research Gap and Contribution in the
Literature.Our contributions to the existing studies are as follows.First, our work investigates the dynamic structures, efficiency, and robustness evolution of the air cargo network from a spatialtemporal perspective, which is lacking in the previous literature.Second, we remove edges instead of nodes as the attack strategy because of its practicality, since even in the extreme case of the COVID-19 global pandemic, most 2 Complexity airports still operate with limited capacity instead of completely shut down.ird, we assess the dynamic evolution of the USACN structure, efficiency, and robustness using longterm data from a spatial-temporal viewpoint, which fills the gaps of research that focus specifically on the air cargo network structures.

Data Selection and Preparation.
e data in this study comes from the US Bureau of Transportation Statistics (https:// www.bts.gov/)website.We focus on the domestic operations of the US air cargo operations from 1990 to 2019.e transportation data is organized into individual tables on an annual basis, which contains the O D information regarding passengers, cargo, distances, carriers, etc., and the total size of the dataset is about 1 Gb.In this paper, we model the USACN as O D networks with the airports representing the nodes and routes that connect the nodes as edges.e raw dataset is subsequently processed to build the US airport network for each year.Most of the previous literature has considered the air transportation network as unweighted and undirected, and we take similar approaches as [3,66,67], where the networks are modeled as directed and weighted.e rationale behind such depiction is that an unweighted network could present bias caused by the prevalence of network topology.In processing the data, we combine the passenger-cargo with the all-cargo hauls and assume that all the passengers carry 23 kg of luggage in the combination of the freight and mail on board and consider this as the total volume that one aircraft can carry.To illustrate the temporal changes in both networks, we perform analyses of cargo flow and classify airports using community structures in 1990, 2000, 2010, and 2019, respectively.Second, we examine the efficiency for the overall and largest community structures each year.ird, we calculate robustness to explore the structure impacts of each attack strategy.

Centrality Indices and Network
Fragmentation. e degree of an airport i represents the number of flights/routes connected to it, which determines its connections to the rest of the network; in other words, the airports with higher degree values connect with more airports.
Betweenness centrality (bc) measures the probability of a node that is on the shortest paths of the other two nodes, reflecting the node's transit capability.In other words, a node with a higher bc is more likely to be a connecting hub, where σ st (i) is the total number of the shortest paths between nodes s and t that pass through i, and σ st is the total number of the shortest paths between s and t that pass through i, and it is expressed as [68] Closeness centrality (cc) measures the average distance from a given starting node to all other nodes in the network, expressed as (2)

Network Community Structures.
is community structure refers to vertices or nodes that cluster into several groups in which nodes are more concentrated within each group than among groups.In air transportation networks, community structures can detect the geographical clusters of airports by measuring the intensity of the flow amongst cities, and the spatial pattern of airports distribution.Specifically, we extract the fragmentation and structure of the air cargo network by measuring the largest community structure (lcs) based on the modularity class m [69,70].e higher the modularity value, the tighter the connection of the network.Furthermore, the decomposition of the network into a set of subgraphs C i , which has a unique value of MR (modularity resolution) associated with this partition, can be measured as follows [71].
e modularity value MR ∈ (−1, 1), which measures the density of links inside communities as compared to links between communities.In a weighted network, it is defined as where a ij represents the cargo volume between two airports i and j, k i �  j a ij is the total cargo volume of the flights of the airport i, c i represent the airport i is located in, the δ function δ(u, v) is 1 if u � v, and 0 otherwise, and m � (1/2) ij a ij .By measuring MR, we can identify both the number and the size of the subgraphs and reveal the geographical characteristics.

Robustness Assessment.
In air transportation, robustness is defined as the ability to remain functional from the loss of critical airports and routes [72,73].In this paper, we assess the network robustness by removing nodes based on their centrality values and obtain the rest iteratively until there is no largest connected component remaining.We constructed a Network Integrity Index (R) to explore each cross-sectional data when that moment occurs.According to [74], ‫ه‬n a weighted network, the robustness of a weighted network can be expressed as a function of the fraction of nodes (airports) removed.Hence, where N is the total number of airports in the network at a given moment and C(F) represents the largest connected community structure when F � fn edges are removed from the network.Consequently, the removal of key routes between airports in the network would dramatically reduce the resilience of the network.Subsequently, the lower the R value, the less the resilience of the network.

Network Efficiency.
e network efficiency is defined as the average value of the reciprocal of the path lengths Complexity between any two nodes in a network [75].In this context, we use the Dijkstra algorithm to calculate the shortest paths between nodes.Mathematically, when nodes i and j are not connected, d ij � +∞, and therefore, (1/d ij ) � 0. In this study, we define the mean value of efficiency between all nodes in the network, which is expressed as Here, N is the number of nodes in the current network.In general, the shorter the path lengths of the route (edge), the more efficient the network.E ∈ (0, 1), where 0 represents a completely disconnected graph and 1 represents a fully connected graph under the ideal condition.

Evolution of USACN Structure and Properties
is study employs Gephi, QGIS, ArcGIS, and python for processing data and representing findings, and the data is available online, and therefore the process is replicable.e findings of this study are presented as follows.

Complex Network Properties.
We discover that the USACN has grown more complex during the study period.As seen in Table 1, both the nodes and edges number increased drastically.Further, the network density has increased by 157% from 7 to 18, which suggests that, on average, one node connects to 7 other nodes in 1990 and 28 other nodes in 2019.Additionally, the average path length has increased from 1.814 to 2.343, indicating that, on average, the air cargo needs to travel for a long distance from one airport to another.Specifically, L � 2.343 in 2019 suggests that, in the 279-airport system, cargos can reach any other airport by two transfers on average.e high clustering coefficient indicates that an airport's topological neighbors are also likely to be connected.Furthermore, we discover that the average path length L is relatively short and close to the value of the random network L rand , and the average clustering coefficient C ≫ C rand , indicating that USACN has small-world [76,77] and scale-free properties.
We have also explored the evolution of the in-degree (k in ) and out-degree (k out ). Figure 1 suggests that both k in and k out conform to a power-law distribution, which indicates that there are hierarchical structures for both in the USACN.In other words, few airports with high centrality values serve as transfer hubs in the network and connect with a majority of airports.e top airports with high k in and k out include Memphis, Louisville, and Anchorage, along with passenger hubs such as Atlanta, Dallas, Chicago, and Denver because the belly-cargo still plays a vital role in transporting goods as passengers travel.

Network Topography and Community Structure.
Figure 2 suggests that the USACN has expanded toward the Rocky Mountains from the coastal regions, and both networks' primary hubs are in the Southeast, Midwest, and Southwest regions, partly due to the geographical advantages of being able to reach major metropolises within a few hours after the overnight sorting process from the air cargo processing facilities.Tables 2-5 further illustrate the shifts of top airports based on centrality rankings from the study period.
e transition of key airports in the USACN is because of the crucial roles of FedEx and UPS in the US domestic air cargo industry.According to the Department of Transportation Bureau of Statistics (USDOT BTS) data, in the year 2019, before the global pandemic, the market share of FedEx and UPS combined is 69.6%.Even during the global pandemic of COVID-19 in 2020 and 2021 (up to June 2021), the two integrators account for 67.7% of the total market share, which further vindicates the critical roles of FedEx and UPS in the air cargo sector.
Communities are clusters of strongly connected nodes, and the communities are interconnecting with few links.
Figure 3 portrays the evolution of the community structures of the USACN from 1990 to 2019.We discovered that the airports in each community have strong ties within their geographical vicinity.Part of the reason for such spatial formation of the network structure is to minimize the transaction cost and maximize fuel efficiency when flying amongst sorting facilities and distribution centers.Consequently, we label each community based on its geographic region.Additionally, the number of communities increased slightly from 27 (36%) in 1990 to 42.45% in 2019.In the meantime, the cargo volume transferred through the largest LCS has risen from 27% to 30.68%, indicating that while the LCS is populous of the maximum number of airports, the emerging airports serve as transshipping hubs that play an increasingly important role in the air cargo network.e Midwest and Southeast regions have the largest community structures throughout the years, which includes the airports including both air cargo and passenger hubs such as, Atlanta, Memphis, Louisville, Dallas, Chicago, Detroit, Charlotte, Indianapolis, and Minneapolis-St.Paul.

Network Efficiency and Robustness Assessment
5.1.Network Efficiency.Contrary to previous studies, we discovered that the global efficiency E was 0.7 in 1990 and decreased to 0.4 in 2019, indicating a decrease in transferability of the USACN, as shown in Figure 4. is is because the USACN has established a hierarchical hub and spoke structure, as most of the connections amongst airports go through central hubs, sorting facilities, and regional warehouses instead of point-to-point routes.It is more economical for the integrators to consolidate their resources and facilitate the growth of the hubs to exploit the density economies.
As for each year, we adopt sequential attacks based on centrality metrics, and we recalculate the metric iteratively until the collapse of the network.We discovered that, in each year, the hub airports usually (a) have higher betweenness and degree centrality since such airports usually have high k in and k out , and strong capability for transferring, such as Memphis, Chicago, and Atlanta, and (b) they have no complementary airports.In other words, when connections 4 Complexity

Complexity
to those airports are closed, there are no alternatives.For example, one of the most critical airports, Memphis in the Southeast region, connects to many other smaller airports across the country, and when such an airport closes, it is difficult to find a replacement airport that is capable to handle the cargo volume.In comparison, airports with tight connections and smaller centrality values such as Philadelphia (PHL) and Newark (EWR) can be the alternative to each other, and therefore closing one would have less impact on overall network efficiency and robustness.When one such airport closes, the other can serve as a bridge to assist the cargo transfer.

Network Robustness.
We assess the robustness of the USACN against the edge removal strategy and portray the spatial structure in Figures 5 and 6.We have the following findings according to the results:            6 represents the attack process based on bc from 1990 to 2019.e size of the nodes represents the bc of the airports.e horizontal axis represents the network spatial structure after a 20% increment of routes removed.e vertical axis represents the years.Geographically, the longdistance route in the noncontiguous regions and remote areas are vulnerable when the flights are disconnected since they do not have alternative routes to reconnect with the rest of the network.Additionally, we discover that the network density is higher in the Southeast, Northeast, Midwest, and Southwest regions, and therefore it is relatively easier for airports in those regions to reroute their cargo to a nearby location within the geographical vicinity; thus, the cs in those regions are more robust.

Conclusion and Remarks
is study examines the evolution of efficiency and robustness of the USACN in the context of a spatiotemporal perspective by portraying it as a directed and weighted network.We adopted the complex network theory to calculate the network efficiency and robustness.Our results reveal that (1) the US air cargo network grew increasingly distinctively to the air passenger counterpart.(2) e airport community structures tend to form close to their geographical proximity.Furthermore, such structure formation is primarily driven by economic reasons such as more efficient sorting facilities and lower transaction costs.With the increasing outreach of the air cargo industry, the number of communities has increased.(3) Owing to the strong dependency of the hub-and-spoke structure, the overall network efficiency decreased from 0.7 to 0.41.Consequently, (4) attacks based on betweenness centrality values are the fastest way to cause network paralysis.Regardless, with the continuous expansion of the network, the overall robustness of the network increased over the years.e network becomes completely disconnected when 60% (45 airports in 1990 and 162 in 2019) of routes are disabled.Geographically, the most vulnerable airports are in the noncontiguous regions such as Hawaii and Puerto Rico.Since those places have long distance and few alternative flights, therefore they would suffer most from the removal of edges, whilst, in the lower 48 states, airports in the Rocky Mountain region are more vulnerable compared with the Southeast and the coastal regions because of the low-density network.rough the analysis, we managed to extract the trunk network of the US air cargo network based on their centrality values and discovered that the evolution of the USACN is similar to other transportation networks such as railroads and subway networks, which exhibits the Matthew effect [78], indicating that new nodes tend to connect to existing high-degree nodes and conform to a hub-and-spoke network structure.Further, the US air cargo network is also subjected to strong spatial constraints and such that nodes are conterminous in space and form a spatial adjacent community structure, though air cargo is less restrained by space, with an average distance of 1000 km throughout the years, which translates to 2-hour flight from source to destination and can cover most of the air cargo integrators' sorting facilities.
In addition to the empirical findings, we also propose several possible managerial insights as follows.First, the hub-and-spoke network structures for both passengers and cargo networks need to be scrutinized by policymakers and investors in the new era of the global economy, especially those airports with smaller degrees and in remote regions.
ough the disconnections of such regions would not severely reduce the overall network efficiency nor the robustness, it would significantly damage the local and regional livelihood not only in the air transportation industry-related fields but also in local manufacturing sectors that depend on air transportation.In the meantime, it is also crucial for the policymakers and investors to take, scrutinize, and reevaluate the role of the airports that have higher centrality values.Additionally, we find that the network is robust against the edge removal strategies, and the closure of the airports with high centrality values, such as Memphis, Louisville, Chicago, and Anchorage, would incur severe damage to the network structure integrity and performance.
ird, as seen in this study, both the efficiency and robustness of the largest community structures have increased, and thus in the future adjustment of network structure, decision-makers should direct more attention to the development of regional hubs to foster network integrity.

Figure 1 :
Figure 1: Evolution of cumulative in-degree and out-degree of the USACN from 1990 to 2019.

Figure 2 :
Figure 2: Evolution of the USACN network structure from 1990 to 2019.

Figure 4 :
Figure 4: Evolution of the USACN efficiency under attacks based on centrality values from 1990 to 2019.

Figure 5 :
Figure 5: Evolution of USACN robustness under attacks based on centrality values from 1990 to 2019.

Figure 6 :
Figure 6: Robustness of the USACN under attacks based on betweenness centrality from 1990 to 2019.

Table 2 :
Rankings of the US air cargo airports based on complex network metrics in 1990.

Table 3 :
Rankings of the US air cargo airports based on complex network metrics in 2000.

Table 4 :
Rankings of the US air cargo airports based on complex network metrics in 2010.

Table 5 :
Rankings of the US air cargo airports based on complex network metrics in 2019.
Southeast, Southwest, and Northeast cs Mideast, Northeast, and Pacific cs Pacific, Southwest, and Northeast cs Top 3 US air cargo network community Structure 1990 We find that the network integrity depends on 60% of the routes, and further removal of routes would result in the robustness dropping to nearly zero.Additionally, the attacks based on degree, bc, and cc have similar effects on the overall network robustness.And we find that attacks on robustness are the fastest way to cause complete network paralysis.