A connectivity-based approach to evaluating port importance in the global container shipping network

This paper proposes a framework for evaluating the strategic importance of container ports based on their connectivity. The Container Port Connectivity Index is computed and decomposed into components according to the Liner Shipping Connectivity Index—each reflecting its contribution to the overall port importance score. The framework produces separate scores for each component, thus allowing port stakeholders to better comprehend why a particular port has become important, and for what reasons. The decomposition approach also allows more detailed analyses, and explanations of the impacts of major economic phenomena—i.e., the expansion of Panama Canal or the crumbling of Hanjin shipping—on the relative importance of ports within the Global Container Shipping Network, as more explanatory variables become available. Our computational results indicate that, while the connectivity of ports related to these events is impacted, changes on connectivity rankings could be adequately explained by the proposed decomposition scheme. The inbound connectivity of New York, for example, was slightly improved after the Panama Canal expansion—from the 29th place in Q1/2016 to the 24th place in Q2/2016—due mainly to the rise in the larger capacity of ships calling. However, in Q3/2016, its inbound rank returned to the 29th place, which was mainly due to the decline in the number of liner services available, number of liner companies, and number of ships calling. The effects of Hanjin’s bankruptcy, on the contrary, were more localized and relatively brief.


Introduction
The strategic importance of a port can be defined by several metrics depending on perspective. Port performance indices, for instance, are traditional measures of port importance, although they consist merely of local statistics that reflect handling capability. To include more detailed information regarding location and connectivity, others have proposed a number of systematic measures that reflect a port's unique characteristics from a network perspective (see Ducruet et al. (2010); Kaluza et al. (2010); Kölzsch and Blasius (2011) for more details). Examples include degree centrality, closeness centrality, betweenness centrality, eigenvector centrality, port cooperative index (Low et al. 2009), and network connectivity index (Tang et al. 2011). While all of these emphasize connectivity, and so the importance of ports, based on network topology-mostly described by shortest paths and shortest path distances-they do not directly reflect the economics of the shipping industry, where distance is not the most important determinant of trade flows (Wilmsmeier and Hoffmann 2008).
The United Nations Conference on Trade and Development (UNCTAD) has established the well-known Liner Shipping Connectivity Index (LSCI) (Hoffmann 2005). Technically, the LSCI is an aggregation of five statistics: (i) number of liner services calling, (ii) number of liner companies, (iii) number of ships, (iv) combined capacity of ships in TEUs, and (v) the largest capacity of ships calling-computed by a simple normalization scheme. Since the LSCI focuses on the accessibility of a country to global trade, economists have found it useful as a joint measure of trade facilitation and maritime connectivity (Bartholdi et al. 2016).
While meaningful, the LSCI is of limited use, especially in a more detailed analysis, as it reduces the global network of container shipping into a two-node network-one for the country of interest and another for the rest of the world (Bartholdi et al. 2016). To utilize this idea at a more granular level, Hoffmann et al. (2014) and Hoffmann et al. (2019) have extended the computation of LSCI to bilateral trade, reflecting trade intensity between two nations. The UNCTAD later applies this same concept to port level-with one additional component, namely the number of connected ports via direct liner shipping services-for the development of Port Liner Shipping Connectivity Index (PLSCI). The PLSCI could be approximately used as one of port connectivity measures, complementing its previous version at country level, although it merely records direct liner shipping services from a port to its immediate neighbors, i.e., port degree.
To better integrate both network topology and economic information into one single framework, Bartholdi et al. (2016) have recently developed a multifaceted port connectivity measure called the Container Port Connectivity Index (CPCI), based on the renowned Hyperlink-Induced Topic Search (HITS) algorithm (Kleinberg 1999). According to this, the LSCI between a pair of ports is first calculated as link weight, reflecting rate of container capacity moving between ports. Once the Global Container Shipping Network (GCSN) is constructed, each port is then assigned two types of importance scores, expressing their relative prominence in terms of both inbound and outbound connectivity. Conceptually, ports with higher inbound and outbound scores are those having greater power to aggregate and distribute goods throughout the network, respectively. As measured by the CPCI, the most important ports are not necessarily those with the most links nor those handling the most TEUs, but rather the ones with good connections with other well-connected ports. This reflects the fact that port connectivity depends not only on the number of links but also on link quality and the connectivity of ports to which they connect (Wang and Cullinane 2016).
Considering the practicality of the CPCI, this paper aims to provide a more finegrained analytical framework based on its extension, where the CPCI is decomposed into elements according to the LSCI. With this framework, we can better comprehend why a particular port has become important, and by which factors. This also allows us to explain the dynamics of port connectivity as a result of the GCSN evolution. To this end, the connectivity of ports is related to two main events in the maritime industry, namely the expansion of Panama Canal and the bankruptcy of Hanjin shipping. Our results indicate that, while the connectivity of ports is impacted by such events, the changes in their connectivity ratings could be adequately explained by our decomposition scheme.
The rest of this paper is organized as follows: A brief review of centrality and connectivity measures is provided in Sect. 2, followed by a discussion of our port connectivity decomposition approach in Sect. 3. All computational results are provided in Sect. 4. Section 5 concludes, highlighting possible future research directions.

Centrality measures
The concept of port connectivity is closely related to the concept of centrality in social science, where centrality measures are frequently used to identify influential nodes in the networks (Wang and Cullinane 2016;Ducruet 2020). Accordingly, many centrality measures have been recently devised and approximately used as connectivity indices in various transportation networks-including, networks of airports , subways (Derrible and Kennedy 2010;Cats 2017), and ports (Kaluza et al. 2010;Kölzsch and Blasius 2011).
Although there is a great number of centrality measures in the literature, many of them could be regarded as variants of the three main classical centrality measures below (Freeman 1978;Friedkin 1991;Borgatti and Everett 2006).
Degree Centrality. This is the simplest centrality measure, used for assessing the importance of a node, based on the number of its immediate neighbors. Mathematically, given a network G = (V,E), where V is a set of nodes and E is a set of edges, degree centrality of node i, denoted by C D (i), could be calculated by Eq. (1).
where a ij equals 1 if there is an edge connecting nodes i and j; and 0, otherwise. When direction is also of interest, in-degree and out-degree centrality can be further defined. Observe that, as degree centrality of a node is independent of the others', degree centrality is sometimes referred to as a measure of intermediate effect.
Closeness Centrality. Closeness centrality is defined by the reciprocal of the sum of shortest distances from a node of interest to the rest of the network. A node with high closeness centrality is therefore the one that is relatively closer to the rest. Formally, closeness centrality of node i, denoted by C C (i), could be computed by Eq. (2).
where d(i,j) is the length of the shortest path from node i to node j. It is worth remarking that, when a network is not strongly connected, i.e., fragmented networks, closeness centrality cannot be well defined, as there might be some node j ∈ V with d(i,j) = ∞. In such cases, we need to redefine d(i,j) to the shortest path length from node i to reachable node j ∈ V. Similar to degree centrality, we may further define closeness centrality based on the directions of shortest paths. In the literature, closeness centrality is also known as a measure of information spread.
Betweenness Centrality. The concept of betweenness centrality is based on the observation that the communication between a pair of nodes depends on a set of nodes that lie between them. Thence, a node that lies on many shortest paths might be considered the most central one. In the literature, betweenness centrality is typically referred to as a measure of information control-where the most central node could be viewed as the most important information gateway. Equation (3) below shows the mathematical expression of betweenness centrality of node i, denoted by C B (i).
where g jk is the number of shortest paths connecting nodes j and k, and g jk (i) is the number of shortest paths connecting nodes j and k passing intermediate node i.
While intuitive, these classical centrality measures, together with their variants, rely too much on assumptions regarding the trajectory of information flow (i.e., the shortest path assumption) and the method of information spread, which results in a less practical use (Borgatti 2005). By properly altering these assumptions and at the same time including more relevant network topology as a part of the computation, more informative centrality measures, such as eigenvector centrality, could be defined.
The main feature that differentiates eigenvector centrality from others is the way centrality is defined. Formally, eigenvector centrality is a function of interactions among nodes rather than the intrinsic property of a node itself (Borgatti and Everett 2006;Kiss and Bichler 2008). A broader class of eigenvector centrality is also known as spectral centrality (Perra and Fortunato 2008), including the prominent Google's PageRank (Bryan and Leise 2006;Langville and Meyer 2006), the HITS algorithms (Kleinberg 1999), the Container Port Acessibility Index (Wang and Cullinane 2008), and the CPCI (Bartholdi et al. 2016).

Port Connectivity Measures.
In the context of container shipping, centrality measures have played an important role as proxies for port importance/connectivity. Kaluza et al. (2010) and Kölzsch and Blasius (2011), for instance, have utilized distance-based centrality measures to identify important ports in a global ocean shipping network that contribute greatly to the bioinvasion of marine organisms. Jiang et al. (2015), In addition to the aforementioned research, Jiang et al. (2015), , and Martínez-Moya and Feo-Valero (2020), alternatively viewed port connectivity as a result from various measures combined, and applied such a concept to different network settings. In particular, Jiang et al. (2015) defined port connectivity as a blended measure between transportation time and capacity, reflecting the strength of ports in the network of container shipping. Based on their ranking, Singapore was ranked first, followed by Busan, while Hong Kong was ranked much lower at the seventh place. , on the other hand, adopted TOPSIS (Technique for Order Preference by Similarity to Ideal Solution), to establish an overall connectivity index for rating three hub ports in Bohai Bay, China. Lastly, Martínez-Moya and Feo-Valero (2020) developed an integrated measure to assess foreland connectivity of Spanish ports, based on both qualitative and quantitative variables. The authors also proposed a decomposition scheme, disintegrating the resulting measure by destination markets. According to their study, a port's geographical location was found to be the determinant of its foreland connectivity, as ports with better geographical locations reduce transit times while offering new trading opportunities within and across regions.
Notwithstanding the usefulness of these contemporary connectivity measures, Wang and Cullinane (2016) asserted that the relative importance of a port should be determined not only by local information-such as port statistics, number of connecting links, or number of shortest paths-but also by network structure and the quality of port connections. Besides, measures with strict assumptions, either on the trajectory of trade flow or port attributes, tend to misinterpret the relative importance of a port within a shipping network, which may eventually lead to a controversial rating. For example, the most central port reported by Kaluza et al. (2010) was Panama Canal followed by Suez Canal, 1 while Hong Kong was not even found in the list of the top twenty most central ports. This disagrees notably with the findings of Bartholdi et al. (2016), where Hong Kong is ranked first in terms of both inbound and outbound connectivity.
While it is difficult to compare and make a fair judgement on different ranked lists, as no or little benchmarking connectivity assessment does exist in the literature (Wang and Cullinane 2016), Ma et al. (2016) and Bao et al. (2017) have recently introduced two interesting indices that allow us to assess the uniqueness of a ranked list and the concordance between a pair of ranked lists, called the monotonicity index and the Kendall's tau rank correlation coefficient, respectively. In terms of uniqueness, the monotonicity index of a ranked list X, denoted by M(X), could be computed by Eq. (4).
where N and N c are the length of ranked list X and the number of nodes with the same index value c ∈ V. According to Eq. (4), if X is perfectly monotonic, i.e., each node is assigned a unique index value, M(X) = 1; else, M(X) will be lying between 0 and 1. Clearly, a measure with high monotonicity value is preferable as it has better distinctive power.
The Kendall's tau rank correlation coefficient (τ), on the other hand, is a measure of concordance between two ranked lists X and Y. In particular, given a randomly selected joint observation pair from X and Y, denoted by (x i ,y i ) and (x j ,y j ), (i) if x i > x j and y i > y j , or x i < x j and y i < y j , the observation pair is said to be concordant, (ii) if x i > x j and y i < y j , or x i < x j and y i > y j , it is said to be discordant, and (iii) if x i = x j or y i = y j , such a pair is neither concordant nor discordant. Based on the numbers of concordance (N 1 ) and discordance (N 2 ), the value of τ could be computed by Eq. (5).
where N denotes total number of observation pairs. If the value of τ is close to 1, the ranked lists X and Y are said to be strongly and positively correlated. In contrast, when the value of τ is close to -1, both lists are weakly and negatively correlated. Considering these recent developments, a comparative study on different measures and their respective ratings could be therefore conducted (see Appendix 2 for the comparison across different measures).

Port connectivity decomposition approach
Let G = (V,E) be the Global Container Shipping Network (GCSN), where V and E denote a set of container ports and a set of links connecting pairs of ports with trade intensity as computed by the LSCI. The CPCI could be determined by the solution to Eqs. (6) and (7).
where L, λ, x and y denote the LSCI matrix, the principal eigenvalue of L, the inbound CPCI vector, and the outbound CPCI vector, respectively.
While the CPCI could reveal the relative importance of ports in terms of both inbound and outbound connectivity, it unfortunately lacks explanatory power in identifying determinants of port importance-as there is only one explanatory variable, namely the LSCI, that dynamically changes with respect to either economic or political occurrences. To strengthen the practical use of the CPCI while preserving its distinctive feature, a connectivity decomposition approach is herein proposed, where the CPCI is disintegrated into components-each reflecting its contribution to the overall port importance score. In doing so, Eqs. (6) and (7) are replaced by Eqs. (8) and (9), as follows.
where C i denotes the ith component of the LSCI in matrix form, i.e., C1 denotes number of liner services calling, C2 denotes number of liner companies, C3 denotes number of ships, C4 denotes combined capacity of ships in TEUs, and C5 denotes the largest capacity of ships calling.

CPCI decomposition
To investigate the relative importance of container ports at a more granular level, the proposed decomposition approach has been applied to the GCSN, whose node and link represent a unique container port and the existence of a scheduled container service traveling from port i to port j. Furthermore, each link is assigned a weight based on the value of LSCI-computed by the data from www. BlueW aterR eport ing. com. With this network setting, Tables 5 and 6 in Appendix 1 report the top 20 ports with highest inbound and outbound scores, together with their LSCI component-wise ratings in Q3/2011 and Q4/2016, respectively.
From Table 5 and 6, we can now comprehend the components of the LSCI that help ports claim higher ranks. For instance, in terms of inbound connectivity (Table 5), Los Angeles and Long Beach are ranked well below other ports by components C1 (number of services liners calling), C2 (number of liner companies), and C3 (number of ships). Nevertheless, Los Angeles and Long Beach are still presented within the top 20 highest scoring ports due to their relatively high importance in the remaining components. Similar interpretation could be made in the case of Qingdao (Table 6), whose outbound CPCI is deteriorated by the component 'largest capacity of ships calling'. We also observe that, among the five LSCI components, component C5, namely, 'largest capacity of ships calling', is highly correlated with the CPCI-based ranking, i.e., the Kendal's tau rank correlation between C5-based ranking and the CPCIbased ranking is the highest. This may be explained by the distributions of these five statistics, where the distribution of C5 shows heavy-tailed phenomenon-unlike the others, showing long-tailed distribution with approximately equal maximum values. With such a distribution, there is bound to be more links with higher C5 values, which, in turn, dominate the ratings by other long-tailed components. In terms of trade, highly ranked ports, implied by the capacity of largest vessels, tend to be, obviously, those capable of accommodating the largest of ships, or equivalently deep-sea ports with better infrastructure and economies of scale.

Impacts of economic phenomena on the connectivity rating of ports
It could be seen from Tables 5 and 6 that the connectivity of ports seems to be more dynamic as it depends not only on the GCSN structure but also on other external factors that could not be captured by most of the connectivity measures in the literature. However, with the decomposition approach proposed here, we show that more detailed analyses, and thus explanations, for the impacts of major economic phenomena on the connectivity rating of ports, could be conducted. To this end, the connectivity of ports related to two main events in the maritime industry, namely the expansion of Panama Canal and the crumbling of Hanjin shipping, is herein explored.

The expansion of Panama Canal
The Panama Canal Expansion was initiated to accommodate the increasing number of container ships that were too large for its earlier infrastructure. By adding a new lane with greater width and depth, the capacity of Panama Canal would be more than doubled allowing larger container ships, typically referred to as the New Panamax-sized vessels, to pass. The new infrastructure commenced operations on June 26th, 2016 and, currently, it is handling containerships that are up to the canal's designed size and capacity.
To properly address the impacts of the Panama Canal Expansion on port connectivity, the changes on both inbound and outbound scores of major ports in the United States and Central American region between Q1/2016 and Q3/2016 have been observed-as over 60 percent of cargo (measured in long tons) passing through the canal either originates from or is destined to U.S. seaports (Bhadury 2016;Wang 2017). These changes are then mapped with their respective connectivity decompositions to identify main contributors, along with insights related to such an occurrence.

The U.S. Coastal ports
As the canal accommodates voyages between ports on the Pacific and Atlantic sides, many major U.S. ports have benefited from such an expansion, especially those on the East Coast and the Gulf Coast-such as the ports of New York, Savannah, and Houston. The reason to this is mainly the introduction of new direct trade routes between the U.S. and Asian manufacturers, without the need of intermodal transportation at the U.S. West Coast ports; something that, in turn, increases inbound connectivity of ports on the East Coast and the Gulf Coast, while reducing that of the U.S West Coast ports. (Bhadury 2016;Liu et al. 2016;Pham et al. 2018;Park et al. 2020).
The inbound connectivity of New York, for example, was slightly improved from the 29th place in Q1/2016 to the 24th place in Q2/2016, due largely to the rise in the largest capacity of ships calling (C5), as illustrated in Table 1. However, in Q3/2016, its inbound rank returned to the 29th place, which was mainly due to the decline in number of liner services calling (C1), number of liner companies (C2), and number of ships calling (C3). From a trade perspective, we may regard this as an adverse effect of the deployment of larger vessels, as more services are expected to be consolidated through vessel sharing agreements among shipping lines, which eventually leads to a decrease in both numbers of ships and ports of call (Harrison and Boske 2017). A similar conclusion could be drawn for Savannah, whose inbound rank jumped from the 93rd place in Q1/2016 to the 79th place in the Q2/2016 and slightly dropped to the 82nd place in Q3/2016 (see Table 1 for more details).
The outbound ranks of New York and Savannah, however, declined from the 68th place and the 35th place in Q1/2016 to the 70th place and the 55th place in Q2/2016, and later dropped to the 119th place and the 117th place in Q3/2016, respectively. Further investigation indicated that many direct connection services from the U.S. East Coast ports to big Asian ports were disappearing, replaced by indirect services calling at nearby ports-such as Colon and Manzanillo, for transhipment before returning to big Asian ports-leading to a big drop in their overall ratings, as reported in Table 2. Similar changes were also spotted in many Gulf Coast ports. The port of Houston, for instance, became much more important in terms of inbound connectivityrising from the 184th in Q1/2016 to the 88th in Q3/2016-due to the increase in the number of trade connections and their respective quality. However, before returning, the vessels tended to call at several intermediate ports for transhipment, leading to a big leap in its inbound rank and a big drop in its outbound rank, as shown in Table 3.
Notwithstanding the positive effects of the Panama Canal expansion on the inbound ranks of U.S. East Coast and Gulf Coast ports, many U.S. West Coast ports in California, Washington, and Oregon were adversely affected as all-water routes to the U.S. East Coast and Gulf Coast ports were cheaper and more competitive when compared to intermodal routes via the U.S. West Coast ports (Woo et al. 2018;Park et al. 2020). Accordingly, less amount of goods was transhipped at these U.S. West Coast ports leading to a drop in their trade intensity-and so inbound connectivity ratings.

Central American Atlantic Coast ports
Close to the Atlantic entrance of the Panama Canal, the ports of Colon and Manzanillo, of Panama, experienced significantly higher trade flows after the expansion of the canal, which was the main reason for the rise in their ranks. More specifically, the inbound ranks of Colon and Manzanillo were improved from the 86th place and the 89th place in Q1/2016 to the 54th place and the 71st place in Q3/2016, while the outbound ranks of these two Panamanian ports also rose from the 134th place and the 118th place in Q1/2016 to the 67th place and the 62nd place in Q3/2016, respectively. According to their connectivity decompositions, number of liner companies (C2), combined capacity of ships in TEUs (C4), and the largest capacity of ships calling (C5) were found to be the main contributors for them in claiming higher ranks. Apparently, more slot capacity was channelled through the canal at these two ports after the expansion. We also observe that, after the expansion, the intensity of trade between these two ports and other major ports in Asia-as well as those on the U.S. East Coast like the port of Savannah-has become more intensified, which further increases their relative prominence as hub ports in their region. Unlike the ports of Colon and Manzanillo, the ranks of nearby ports in the Caribbean Sea, such as the ports of Cartagena and Kingston, gradually dropped from one quarter to the other-although the maximum size of vessels calling at these ports was almost doubled. According to our computational results, these two Caribbean ports suffered badly from weaker trade intensity-and some of their trade connections were replaced by Colon and Manzanillo. However, the roles of these Caribbean ports may be improved in the near future as there are plans to expand them to consolidate freight from both North and South American countries (Harrison and Boske 2017).

Central American Pacific Coast ports
On the other side of the Panama Canal, the inbound rank of Balboa declined continuously from the 95th place in Q1/2016 to the 152nd place in Q3/2016 due to the decrease in all of the first four LSCI components. This finding, along with the rise of Colon and Manzanillo at the Atlantic entrance, indicated that Balboa became less central after the expansion, i.e., more goods were passing through the canal to the ports of Colon and Manzanillo. This was also the case for its outbound connectivity, whose rank declined from the 75th place in Q1/2016 to the 88th place in Q3/2016.
Lastly, the port of Manzanillo, Mexico, slightly benefited from the expansion, as its inbound rank improved from the 42nd place in Q1/2016 to the 41st place in Q3/2016. The port's outbound traffic declined marginally from the 48th place in Q1/2016 to the 49th place in Q3/2016. According to our connectivity decomposition, the increase in Manzanillo's rank was driven by the increase the in number of liner companies (C2), number of ships (C3), and combined capacity of ships in TEUs (C4)-along with its frequent trade connections with the ports of Shanghai and Busan, which better reflected its role as a connection point among ports in Asia, South America, and the Panama Canal.

The Bankruptcy of Hanjin shipping
Hanjin Shipping Co., Ltd., a South Korean transport, aviation (Korean Air), logistics and container shipping company, was the seventh-largest shipping line in terms of capacity before it filed for receivership on August 31st, 2016 and later declared bankruptcy on February 17th, 2017. During these periods, Hanjin's vessels were not allowed to call at many major ports such as Shanghai, Xiamen, Valencia, Savannah, and Long Beach, due to uncertainty in the payment of port access fees. The flow of more than 540,000 TEUs were accordingly suspended in the ocean just to avoid seizure by creditors (Su et al. 2019).
Based on our computational results, the bankruptcy of Hanjin shipping affected the relative importance of ports in which Hanjin operated, especially at Long Beach and Seattle-two main strategic ports of Hanjin in the transpacific services-as shown in Figs. 1 and 2. Regarding inbound connectivity (Fig. 1), Long Beach fell from the 21st place in Q2/2016 to the 25th place in Q3/2016, and later dropped to the 31st place in Q4/2016, respectively. This could be explained by the fact that Hanjin vessels typically called at Long Beach for unloading. But since Hanjin vessels were not allowed to call at such a port, the first four LSCI components of Long Beach declined, leading to the decrease in the port's inbound connectivity rating (see Table 4 for more details). Similar conclusion could be drawn for Seattle (Fig. 2), another Hanjin main port, whose outbound rank fell from the 53rd place in Q2/2016 to the 77th place in Q4/2016 (it should be remarked that, as Seattle is much smaller than Long Beach, and Hanjin played a big role in Seattle, i.e., it co-owned some terminals alongside MSC, Seattle was more vulnerable to the absence of Hanjin).
Besides Long Beach and Seattle, the ranking of other highly rated ports by the CPCI seemed to be unaffected (see Tables 5 and 6), although statistics of the first four LSCI components at these ports declined. Literally speaking, the most central ports, as measured by the CPCI, changed slightly from one quarter to the othereven the port of Busan, one of Hanjin's main ports in Asia. This may be explained by the current shipping environment (Song et al. 2019), whereby the highly ranked ports typically have more service connections when compared to the lower ranked ones. As such, the absence of one shipping line would not severely affect their connectivity-but this is not the case for (smaller) ports that rely heavily on few shipping lines.
Furthermore, the effects of Hanjin's bankruptcy seem to be relatively brief, as the ranks of many ports have returned to their original places in Q1/2017. The reason behind this may be the introduction of new services-or the substitution of services by Hanjin's alliance (Song et al. 2019;Su et al. 2019)-to ports that Hanjin previously operated.

Conclusions
To evaluate the strategic importance of container ports within the GCSN, several connectivity indices have been recently proposed-mostly based on network topology, albeit with the exclusion of economic information. Consequently, they fail to explain economic phenomena within the shipping industry, leading to either contradictive or unjustifiable ratings. To better evaluate a port's strategic importance, we have proposed here a simple decomposition scheme for the CPCI, where the index is first computed as an overall port importance score, and then decomposed into components-each reflecting its contribution to the overall port importance score. Since this approach segregates the GCSN into a five-layer network, each of which representing a component-wise network with its own score, we can then better comprehend why a particular port has become important, and by which factors. To this end, we find that the capacity of largest vessels calling is the most decisive factor for a port in claiming a higher rank, as its distribution shows a heavy-tailed phenomenon-unlike others, showing long-tailed distributions with approximately equal maximum values. This is consonant with the fact that deep-sea ports, capable of accommodating larger ships, tend to be those offering economies of scale and, thus, be considered important global hub ports.
The proposed decomposition approach also allows us to conduct more detailed analyses, and thus explanations of the impacts of major economic phenomena on the relative importance of ports within the GCSN. In particular, we find that the connectivity of certain ports has been affected by the expansion of the Panama Canal and the crumbling of Hanjin shipping. The changes in the connectivity ratings of those ports can be adequately explained by the proposed decomposition scheme, thus validating our approach.
As has been illustrated by these results, it is evident that the ranking of ports evolves dynamically over time due to the changes in the maritime industry. It would be therefore interesting to see in subsequent studies how these revolutions affect the long-term rating of container ports, as well as the formation of trading communities, over a longer period of time.

Appendix 1: Top 20 highest-scoring ports by Inbound and Outbound CPCI
See Tables 5 and 6.     Table 8 The twenty most central ports as measured by degree, closeness, betweenness, and the PLSCI in Q4/2016  (Tables 7 and 8) are relatively more dispersed, especially those of betweenness centrality.

Rank
Regarding the PLSCI, although the number of ports in our data set and that of UNCTAD are somewhat different, the Kendall's tau rank correlation coefficients between the CPCI and the PLSCI indicate that the CPCI is positively correlated with the PLSCI-14 out of the top twenty most central ports ranked by the PLSCI in Q3/2011 and Q3/2016 also appear in the top 20 by the CPCI (either inbound or outbound).
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