# Selecting the Strategic Port of “the Belt and Road” Based on the Global Network

Authors: Zihui Yang; Qingchun Meng; Chanjuan Li
Journal: Complexity
 (2021)

---

## Abstract

Under “the Belt and Road” initiative, China promoted cooperation between domestic enterprises and international ports vigorously, which brought back fruitful results, while the rational selection of strategic pivots ports and the optimization of the layout of the port network are important guarantees to a further promotion to the economic development of “the Belt and Road” ports and give full play to the driving and radiation role of strategic pivots ports. On the basis of constructing a network of 155 ports in the world, according to the number of ports crossed by the shortest path and betweenness centrality in the network, this paper uses K-Medoids clustering algorithm to train the strategic importance of ports and verifies the reliability of the analysis results. On this basis, the joint coverage analysis of strategically important ports is carried out, 17 ports are identified as strategic pivots ports of the global port network, and, finally, based on the two attributes of “the Belt and Road” and “Chinese enterprise participation” of strategic pivots ports, the leading role of strategic pivots ports in geographical location, path coverage, development potential, cooperation stability, and control is analyzed, and instructive suggestions are put forward.


---

## Body

## 1. Introduction

Since China launched “the Belt and Road” initiative in 2013, China’s nonfinancial investment in “the Belt and Road” Agreement countries has exceeded US$100 billion by the end of 2019 (over the past seven years, China’s total imports and exports of goods with countries along “the Belt and Road” have increased to $1.34 trillion[N]. Economic Daily, 2020-09-07), including 103 port cooperation projects involving 94 ports (the original reference is 101 projects involving 90 ports, and this article completes the data until August 2020) [1]. Not only are international ports the foundation and artery of international trade, but also the resulting network is an important platform to promote international industrial integration and optimize the allocation of international resources, and the world in the operation of more than 480 international ports, each port in geographical location, throughput capacity, cargo adaptability, and hinterland countries industrial economic conditions and bilateral trade relations with China and other countries have certain differences. Therefore, in the network of international ports, how to determine the strategic pivots of ports, effectively lay out the global port network, open up a new engine of port economic development, play the leading role of “the Belt and Road” initiative, and further promote the integration of China and “the Belt and Road” countries along the political and economic relations are of great significance.From a global perspective, international politics and economics, as well as global governance and international rules, place new historical demands on “the Belt and Road” initiative’s international cooperation in the areas of global debt and financing, green development, inclusive development, transparency and anticorruption, and third-party market cooperation [2]. “The Belt and Road” initiative is a major strategy for China to implement all-round opening up to the outside world and has built a new platform for mutually beneficial and win-win cooperation for deepening and expanding new sino-foreign cooperative relations, forming a multilevel and multiform pattern of cultural and economic exchanges, accelerating the economic transformation, and upgrading and developing the countries along the path in the new era [3]; based on economic exchanges, political mutual trust, people-to-people exchanges, and civilizational mutual learning, the common development of countries and regions along the path on the basis of “common business, coconstruction, and sharing” has been promoted, and the construction of a community of human destiny in the new era has been accelerated [4]. With the continuous promotion of “the Belt and Road,” the current domestic affairs and contemporary international affairs have been integrated; in order to promote the reform of global economic governance, we must use the development-oriented and practical rationality to strengthen each other’s theoretical thinking, combined with the practice of “development win-win” inclusive globalization operation logic, and put forward the “China Program” of global economic governance with inclusive development mechanism as the core concept [5].From the perspective of national strategy, the essence of the “the Belt and Road” network economy is the logistics and communication network between countries, and its development focuses on the cognition and practice among countries, so the perspective of “the Belt and Road” is the spatial paradigm of network form, not geopolitical strategy [6]. On the one hand, “the Belt and Road” initiative not only is closely in line with China’s national strategic objectives such as national rejuvenation but also achieves the diplomatic goals of “world peace and development” by deepening China’s relations with its neighbors [7]; on the other hand, “the Belt and Road” initiative has promoted changes in economic structure [8, 9], trade patterns [10, 11], and green development [12] along the path, not only easing the tension caused by regional economic development differences but also promoting the development of global economic integration, and to a certain extent curbed terrorism in poor areas [13]. In addition, the industrial transfer of countries along the Belt and Road is mutually beneficial to the upgrading of bilateral or multilateral value chains, and symbiosis is an important transmission path to promote industrial transfer in countries along “the Belt and Road,” including China [14].The strategic pivots are the apes of a particular network that has greater influence and control over the entire network. In the network of countries along “the Belt and Road,” strategic pivots countries not only have the basis and influence to promote strategic position, the radiation capability, common interests, level of bilateral relations, and so on [15] but also have special geographical status, economic demonstration role and key strategic values, and other basic functions [16], while in the strategic pivots city of space structure network [17, 18], the strategic pivots industry in complex structural networks [19] needs to be strategic enough to play a strong leading role. The pivots of maritime strategy have always been the hot direction of academic research, which is beneficial to realizing the layout of overseas port construction from a global perspective and to the investment construction of overseas port [20]; as a fixed supply point, rest point, and ship aircraft berth repair point overseas, the maritime strategic pivots are crucial to maintaining maritime transport security, promoting practical cooperation at sea, and realizing the strategy of maritime power [21], but the maritime strategic pivots are not only a strategic hub at sea but also a strategic channel, and strategic maritime areas are structurally and spatially different [22], which requires an overall optimization of the layout of the marine strategic network to lay the foundations of the marine security and economic strategy [23, 24].From the abstract network point of view, the betweenness centrality of vertexes [25] and adaptive merest centrality [26] are the important basis for selecting the strategic pivots of the network, the port industry network covers a wide range, the situation is more complex, and the problems are endless [27], but the port industry is an important index to realize the development of the port; from the perspective of the global port system, the shipping network, and hub port space pattern, strategic pivots port is bound to be the main hub and important channel of the maritime shipping network system [28]; it has a great influence on the analysis, as collectivity, accessibility, and interconnectedness of coastal port networks in various countries [29]; from the spatial contact and regional difference panel data of the shipping network in the past 10 years, the global ocean shipping adversity coefficient has been gradually improved, the average path length of shipping has been gradually shortened, and the functional difference of transit connection is getting smaller and smaller [30], but the existing maritime distribution network has been shown to meet the rapid growth of cargo throughput [31], with higher requirements for line network and connectivity measurements, as well as for the efficiency of shipping and port operations [32]. The selection of strategic pivots such as other transportation networks [33], aviation logistics networks [34], and passenger flow networks also requires measuring the importance and influence of nodes [35].The above research results have laid a good foundation, but the “the Belt and Road” initiative has not been put forward for a long time; the relevant experience data are relatively scarce, so its academic research is still in its infancy, the systematic research results are less, especially for the global port network strategic pivots selection, and optimization results are much rare. Under the “the Belt and Road” initiative, based on the fruitful results of domestic enterprises participating in international port investment, construction, and operation, how to find strategic pivots ports, optimize the layout of the port network, and promote the port economic development of countries along “the Belt and Road” is particularly important.


## 2. The Setting and Processing of the Basic Data of the Port Network

Set the port network vertexes, edges, rights, and other basic data, and carry out the following steps to process them.


### 2.1. Port Sample Selection

#### 2.1.1. Alternative Conditions Setting for Port Samples

In order to ensure that port sample data are covert, targeted, and important, alternative port sample selection ensures several principles: ensuring that countries along the main sea paths have port access to alternative samples, ensuring that alternative samples are accessed by the world’s major maritime ports, basically ensuring that the Belt and Road Agreement countries have alternative samples for port access, and basically ensuring that ports have access to alternative samples for each maritime area.To this end, the following alternative port samples are proposed: (1) ports in which Chinese enterprises are involved in investment, construction, and operation are all included in the alternative port sample; (2) the largest ports of the countries along “the Belt and Road” path are included in the sample of alternative ports; (3) when “the Belt and Road” countries span multiple maritime areas, ensure that each of the countries has at least one sample of alternative ports in each marine area; (4) the ports in the top 40 in world throughput in 2019 are used as samples of alternative ports.


#### 2.1.2. Noise Reduction of Alternative Port Samples

In order to ensure the validity of the data and the time-ability of simulation verification, the alternative port samples were optimized for the noise reduction, excluding port samples that clearly did not meet the strategic pivots requirements, and the noise reduction conditions were as follows: (1) ports of island countries that did not enter the top 100 in 2019 were not considered as alternative samples; (2) there are no more than two alternative samples of a country’s ports in the same sea area from the same continent.


#### 2.1.3. Port Sample Results

After the selection and optimization of the port samples in the above two steps, 155 alternative port samples are obtained, as in Table1.Table 1
List of alternative port samples.
AreaAlternative PortsAsia (45)Shanghai Port, Guangzhou Port, Hong Kong, Kaohsiung Port, Hanoi Port, Da Nang, Sihanoukville, Bangkok Port, Laem chabang, Kuantan Port, Melaka Gateway, Kuala Selangor, Penang Port, Singapore Port, Manila Port, Abu Dhabi Port, Gwadar Port, Yokohama Port, Chongjin Port, Busan, Dhaka Port, Chattogram Port, Kyaukpyu Port, Colombo Port, Hambantota Port, Mumbai Port, Chennai Port, Istanbul Port, Qishm, the Port of Chahbahar, Dammam Port, Jeddah, Doha Port, Salalah Port, Aden Port, Haifa Port, Jakarta-Kariburu, Jambi International Port, Tanjung Priok, Jerusalem Port, Batumi Port, Kuwait Port, Nicosia Port, Basrah Port, Lattakia PortAfrica (37)Tunisia Port, Cherchell Port, Suez Port, Damietta Port, Por Said Port, Luanda Port, Bata Port, Lome Port, Masawa Port, Pointe Noire Port, Matadi Port, Djibouti Port, Boke Terminal, Conakry Port, Tema Port, Kribi Port, Abidjan Port, Mombasa Port, Tamataf Port, Dakar Port, Monrovia Port, Gentil Port, Cotonou Port, Tangier Port, Dakhla Port, Nouakchott Port, Beira Port, Maputo Port, Walvis Port, Lagos Tingcan Port, Sao Tome and Principe Port, Sudan Port, Dar es Saalam Port, Tripoli Port, Berbera Port, Cape Town Port, Durban PortEurope (33)Hamburg Hafen, London Port, Liverpool Port, Le Havre Port, Marseille Port, Lisbon Port, Hammerforst Port, Oslo Port, the Kingdom of Denmark, Stockholm Port, Helsinki Port, Gdańsk Port, Archangelsk Port, Vladivostok Port, Murmansk Port, Nakhodka Port, Sochi Port, Port of Rotterdam, Port of Amsterdam, Antwerp Port, Zebrukh Port, Valencia Port, the Port of Gibraltar, Bilbao Port, Piraeus Port Terminal, Wado Port, San Marino Port, Reykjavík Port, Rijeka Port, Durres Port, Constanta Port, Odessa Port, Varna PortOceania (7)Darwin Port, Melbourne Port, Fremantle Port, Newcastle Port, Lae Port, Wellington Port, Suva PortNorth America (22)Manzanillo Port, Veracruz Port, New York Port, Port of Long Beach, Los Angeles, New Orleans Port, Vancouver Port, Churchill Port, Montreal Port, Havana port, Pilon port, Kingston harbor, Santo Domingo Port, Port-au-Prince, Guatemala Port, Puerto Barrios Port, Honduras Port, Managua Port, Cabesas Port, San Jose Port, Puerto Limon, Colon Port, Panama City PortSouth America (11)Cali port, Barranquilla Port, Guayaquil Port, Kayao Port, San Diego Port, Punta Arenas Port, La Guaira Port, Buenos Aires Port, Paranagua Port, Santos Port, St Louis PortThe above alternative ports, including 79 countries that have signed “the Belt and Road” Agreement, as well as 64 ports in which China is involved in investment, construction, and operation, fully cover the major existing international sea paths and have a broad industry coverage base.


### 2.2. Set the Path between Ports

To set the path between ports is to set the rules for direct connections (direct connection: a straight line between ports) between ports. In order to simplify the calculation and ensure that the port connection is set in accordance with the rules of realistic sea paths, the rules for direct port connections are as follows: (1) All continents are nonnavigational. (2) All waters are navy accessible. (3) There is no transcontinental connection between ports, which is a valid path. (4) A direct connection within a neighboring port on the same continent crosses the continent in which it is located, and the direct connection is a valid path. (5) A direct connection within a port that does not conform to (3) and (4) transverses the continent and is invalid. (6) Ports cannot be connected to themselves.Keep the valid path, cancel the invalid path, and get a connection between the vertexes that are not authorized to be identified by the port network diagram, that is, the path between the alternate ports.


### 2.3. Determine the Distance between Ports

The distance between ports is given to the corresponding effective path, that is, to the edge of the port network. Rules of empowerment are as follows: (1) The right to an effective path is the distance between ports (sea) (available directly at port.sol.com.cn,SeaRates.com, and McDistance shipping calculation tools. If there is a large difference in data between the three queries, the average method is used for optimization). (2) The right of the invalid path is recorded as +∞.The distance of the adjacent port is obtained through the official website and the shipping distance calculation tool (adjacent port distances are available through port.sol.com.cn,SeaRates.com, and McDistance shipping calculation tools), and the average of the three types of data serves as the final distance of the adjacent port. Since the network map of the adjacent port does not cover all ports, there is a certain difference between the shortest path value and the actual value of the nondirect port, but the error is small and the substantive influence on the choice of hub strategic pivots is limited.The direct connection and distance between the alternative ports are determined, and, according to the characteristics of the two-way passage of sea paths, the port network is a nondirectional right network containing 155 vertices, which is recorded asGV,E,C, where V represents the vertexes of G, V=v1,v2,…,v155, E is the edge of G, and C is the right of direct connection. The distance between the alternative ports is represented by a matrix GC, which is the direct distance from port vi to port vj, “null” if the port-to-port is an invalid path, or 0 if the distance is 0, and the distance matrix GC between the alternative ports is represented as(1)GC=c1−1c1−2⋯c1−155c2−1c2−2⋯c2−155⋮⋮⋱⋮c155−1c155−2⋯c155−155=0944.6⋯null944.60⋯null⋮⋮⋱⋮nullnull⋯0.See the Table Port Distance and the Table Port Shortest Path Value (the Distance data between ports can be searched or downloaded from the Table Port Distance and the Table Port Shortest Path Value in the following link:https://doi.org/10.4121/14298851) for specific data.


## 2.1. Port Sample Selection

### 2.1.1. Alternative Conditions Setting for Port Samples

In order to ensure that port sample data are covert, targeted, and important, alternative port sample selection ensures several principles: ensuring that countries along the main sea paths have port access to alternative samples, ensuring that alternative samples are accessed by the world’s major maritime ports, basically ensuring that the Belt and Road Agreement countries have alternative samples for port access, and basically ensuring that ports have access to alternative samples for each maritime area.To this end, the following alternative port samples are proposed: (1) ports in which Chinese enterprises are involved in investment, construction, and operation are all included in the alternative port sample; (2) the largest ports of the countries along “the Belt and Road” path are included in the sample of alternative ports; (3) when “the Belt and Road” countries span multiple maritime areas, ensure that each of the countries has at least one sample of alternative ports in each marine area; (4) the ports in the top 40 in world throughput in 2019 are used as samples of alternative ports.


### 2.1.2. Noise Reduction of Alternative Port Samples

In order to ensure the validity of the data and the time-ability of simulation verification, the alternative port samples were optimized for the noise reduction, excluding port samples that clearly did not meet the strategic pivots requirements, and the noise reduction conditions were as follows: (1) ports of island countries that did not enter the top 100 in 2019 were not considered as alternative samples; (2) there are no more than two alternative samples of a country’s ports in the same sea area from the same continent.


### 2.1.3. Port Sample Results

After the selection and optimization of the port samples in the above two steps, 155 alternative port samples are obtained, as in Table1.Table 1
List of alternative port samples.
AreaAlternative PortsAsia (45)Shanghai Port, Guangzhou Port, Hong Kong, Kaohsiung Port, Hanoi Port, Da Nang, Sihanoukville, Bangkok Port, Laem chabang, Kuantan Port, Melaka Gateway, Kuala Selangor, Penang Port, Singapore Port, Manila Port, Abu Dhabi Port, Gwadar Port, Yokohama Port, Chongjin Port, Busan, Dhaka Port, Chattogram Port, Kyaukpyu Port, Colombo Port, Hambantota Port, Mumbai Port, Chennai Port, Istanbul Port, Qishm, the Port of Chahbahar, Dammam Port, Jeddah, Doha Port, Salalah Port, Aden Port, Haifa Port, Jakarta-Kariburu, Jambi International Port, Tanjung Priok, Jerusalem Port, Batumi Port, Kuwait Port, Nicosia Port, Basrah Port, Lattakia PortAfrica (37)Tunisia Port, Cherchell Port, Suez Port, Damietta Port, Por Said Port, Luanda Port, Bata Port, Lome Port, Masawa Port, Pointe Noire Port, Matadi Port, Djibouti Port, Boke Terminal, Conakry Port, Tema Port, Kribi Port, Abidjan Port, Mombasa Port, Tamataf Port, Dakar Port, Monrovia Port, Gentil Port, Cotonou Port, Tangier Port, Dakhla Port, Nouakchott Port, Beira Port, Maputo Port, Walvis Port, Lagos Tingcan Port, Sao Tome and Principe Port, Sudan Port, Dar es Saalam Port, Tripoli Port, Berbera Port, Cape Town Port, Durban PortEurope (33)Hamburg Hafen, London Port, Liverpool Port, Le Havre Port, Marseille Port, Lisbon Port, Hammerforst Port, Oslo Port, the Kingdom of Denmark, Stockholm Port, Helsinki Port, Gdańsk Port, Archangelsk Port, Vladivostok Port, Murmansk Port, Nakhodka Port, Sochi Port, Port of Rotterdam, Port of Amsterdam, Antwerp Port, Zebrukh Port, Valencia Port, the Port of Gibraltar, Bilbao Port, Piraeus Port Terminal, Wado Port, San Marino Port, Reykjavík Port, Rijeka Port, Durres Port, Constanta Port, Odessa Port, Varna PortOceania (7)Darwin Port, Melbourne Port, Fremantle Port, Newcastle Port, Lae Port, Wellington Port, Suva PortNorth America (22)Manzanillo Port, Veracruz Port, New York Port, Port of Long Beach, Los Angeles, New Orleans Port, Vancouver Port, Churchill Port, Montreal Port, Havana port, Pilon port, Kingston harbor, Santo Domingo Port, Port-au-Prince, Guatemala Port, Puerto Barrios Port, Honduras Port, Managua Port, Cabesas Port, San Jose Port, Puerto Limon, Colon Port, Panama City PortSouth America (11)Cali port, Barranquilla Port, Guayaquil Port, Kayao Port, San Diego Port, Punta Arenas Port, La Guaira Port, Buenos Aires Port, Paranagua Port, Santos Port, St Louis PortThe above alternative ports, including 79 countries that have signed “the Belt and Road” Agreement, as well as 64 ports in which China is involved in investment, construction, and operation, fully cover the major existing international sea paths and have a broad industry coverage base.


## 2.1.1. Alternative Conditions Setting for Port Samples

In order to ensure that port sample data are covert, targeted, and important, alternative port sample selection ensures several principles: ensuring that countries along the main sea paths have port access to alternative samples, ensuring that alternative samples are accessed by the world’s major maritime ports, basically ensuring that the Belt and Road Agreement countries have alternative samples for port access, and basically ensuring that ports have access to alternative samples for each maritime area.To this end, the following alternative port samples are proposed: (1) ports in which Chinese enterprises are involved in investment, construction, and operation are all included in the alternative port sample; (2) the largest ports of the countries along “the Belt and Road” path are included in the sample of alternative ports; (3) when “the Belt and Road” countries span multiple maritime areas, ensure that each of the countries has at least one sample of alternative ports in each marine area; (4) the ports in the top 40 in world throughput in 2019 are used as samples of alternative ports.


## 2.1.2. Noise Reduction of Alternative Port Samples

In order to ensure the validity of the data and the time-ability of simulation verification, the alternative port samples were optimized for the noise reduction, excluding port samples that clearly did not meet the strategic pivots requirements, and the noise reduction conditions were as follows: (1) ports of island countries that did not enter the top 100 in 2019 were not considered as alternative samples; (2) there are no more than two alternative samples of a country’s ports in the same sea area from the same continent.


## 2.1.3. Port Sample Results

After the selection and optimization of the port samples in the above two steps, 155 alternative port samples are obtained, as in Table1.Table 1
List of alternative port samples.
AreaAlternative PortsAsia (45)Shanghai Port, Guangzhou Port, Hong Kong, Kaohsiung Port, Hanoi Port, Da Nang, Sihanoukville, Bangkok Port, Laem chabang, Kuantan Port, Melaka Gateway, Kuala Selangor, Penang Port, Singapore Port, Manila Port, Abu Dhabi Port, Gwadar Port, Yokohama Port, Chongjin Port, Busan, Dhaka Port, Chattogram Port, Kyaukpyu Port, Colombo Port, Hambantota Port, Mumbai Port, Chennai Port, Istanbul Port, Qishm, the Port of Chahbahar, Dammam Port, Jeddah, Doha Port, Salalah Port, Aden Port, Haifa Port, Jakarta-Kariburu, Jambi International Port, Tanjung Priok, Jerusalem Port, Batumi Port, Kuwait Port, Nicosia Port, Basrah Port, Lattakia PortAfrica (37)Tunisia Port, Cherchell Port, Suez Port, Damietta Port, Por Said Port, Luanda Port, Bata Port, Lome Port, Masawa Port, Pointe Noire Port, Matadi Port, Djibouti Port, Boke Terminal, Conakry Port, Tema Port, Kribi Port, Abidjan Port, Mombasa Port, Tamataf Port, Dakar Port, Monrovia Port, Gentil Port, Cotonou Port, Tangier Port, Dakhla Port, Nouakchott Port, Beira Port, Maputo Port, Walvis Port, Lagos Tingcan Port, Sao Tome and Principe Port, Sudan Port, Dar es Saalam Port, Tripoli Port, Berbera Port, Cape Town Port, Durban PortEurope (33)Hamburg Hafen, London Port, Liverpool Port, Le Havre Port, Marseille Port, Lisbon Port, Hammerforst Port, Oslo Port, the Kingdom of Denmark, Stockholm Port, Helsinki Port, Gdańsk Port, Archangelsk Port, Vladivostok Port, Murmansk Port, Nakhodka Port, Sochi Port, Port of Rotterdam, Port of Amsterdam, Antwerp Port, Zebrukh Port, Valencia Port, the Port of Gibraltar, Bilbao Port, Piraeus Port Terminal, Wado Port, San Marino Port, Reykjavík Port, Rijeka Port, Durres Port, Constanta Port, Odessa Port, Varna PortOceania (7)Darwin Port, Melbourne Port, Fremantle Port, Newcastle Port, Lae Port, Wellington Port, Suva PortNorth America (22)Manzanillo Port, Veracruz Port, New York Port, Port of Long Beach, Los Angeles, New Orleans Port, Vancouver Port, Churchill Port, Montreal Port, Havana port, Pilon port, Kingston harbor, Santo Domingo Port, Port-au-Prince, Guatemala Port, Puerto Barrios Port, Honduras Port, Managua Port, Cabesas Port, San Jose Port, Puerto Limon, Colon Port, Panama City PortSouth America (11)Cali port, Barranquilla Port, Guayaquil Port, Kayao Port, San Diego Port, Punta Arenas Port, La Guaira Port, Buenos Aires Port, Paranagua Port, Santos Port, St Louis PortThe above alternative ports, including 79 countries that have signed “the Belt and Road” Agreement, as well as 64 ports in which China is involved in investment, construction, and operation, fully cover the major existing international sea paths and have a broad industry coverage base.


## 2.2. Set the Path between Ports

To set the path between ports is to set the rules for direct connections (direct connection: a straight line between ports) between ports. In order to simplify the calculation and ensure that the port connection is set in accordance with the rules of realistic sea paths, the rules for direct port connections are as follows: (1) All continents are nonnavigational. (2) All waters are navy accessible. (3) There is no transcontinental connection between ports, which is a valid path. (4) A direct connection within a neighboring port on the same continent crosses the continent in which it is located, and the direct connection is a valid path. (5) A direct connection within a port that does not conform to (3) and (4) transverses the continent and is invalid. (6) Ports cannot be connected to themselves.Keep the valid path, cancel the invalid path, and get a connection between the vertexes that are not authorized to be identified by the port network diagram, that is, the path between the alternate ports.


## 2.3. Determine the Distance between Ports

The distance between ports is given to the corresponding effective path, that is, to the edge of the port network. Rules of empowerment are as follows: (1) The right to an effective path is the distance between ports (sea) (available directly at port.sol.com.cn,SeaRates.com, and McDistance shipping calculation tools. If there is a large difference in data between the three queries, the average method is used for optimization). (2) The right of the invalid path is recorded as +∞.The distance of the adjacent port is obtained through the official website and the shipping distance calculation tool (adjacent port distances are available through port.sol.com.cn,SeaRates.com, and McDistance shipping calculation tools), and the average of the three types of data serves as the final distance of the adjacent port. Since the network map of the adjacent port does not cover all ports, there is a certain difference between the shortest path value and the actual value of the nondirect port, but the error is small and the substantive influence on the choice of hub strategic pivots is limited.The direct connection and distance between the alternative ports are determined, and, according to the characteristics of the two-way passage of sea paths, the port network is a nondirectional right network containing 155 vertices, which is recorded asGV,E,C, where V represents the vertexes of G, V=v1,v2,…,v155, E is the edge of G, and C is the right of direct connection. The distance between the alternative ports is represented by a matrix GC, which is the direct distance from port vi to port vj, “null” if the port-to-port is an invalid path, or 0 if the distance is 0, and the distance matrix GC between the alternative ports is represented as(1)GC=c1−1c1−2⋯c1−155c2−1c2−2⋯c2−155⋮⋮⋱⋮c155−1c155−2⋯c155−155=0944.6⋯null944.60⋯null⋮⋮⋱⋮nullnull⋯0.See the Table Port Distance and the Table Port Shortest Path Value (the Distance data between ports can be searched or downloaded from the Table Port Distance and the Table Port Shortest Path Value in the following link:https://doi.org/10.4121/14298851) for specific data.


## 3. The Choice of Strategic Pivots of the Port Network Based on the Number of Ports Crossed by the Shortest Path

The port and path are abstracted into the port network model, the shortest path between the two ports is solved, the shortest path is calculated through the port, the strategic importance of the port is judged as superior or not, and the strategic pivots of the port network are finally selected.


### 3.1. Building a Model about the Number of Ports Crossed by the Shortest Path

Using the Floyd algorithm, the shortest path between two ports in the port network diagram is solved (there may be several shortest paths between the two ports, but this is not the case here, and the results simulated by Python are used as the only final result. The results of the shortest path solution can be searched or downloaded from the Table Port Shortest Path in the following link:https://doi.org/10.4121/14298851). Ports are connected only to each other, not directly to each other, and the shortest path between ports may include, in addition to the port from port to port, the passage through intermediate ports, which together with the port from the beginning constitute the shortest path from port to port. To solve the number of ports crossed by the shortest path, it needs to be solved in three steps.


#### 3.1.1. Determine Whether a Port Is Crossed by a Shortest Path

Determine whether the shortest path from portvi to port vj crossed port vk or not, and remember zkij. If zkij=1, it indicates that the shortest path from port vi to port vj crossed port vk. If zkij=0, it indicates that the shortest path crossed port vk. The judgment vector for the shortest path between port vi and port vj can then be expressed as zkij, where i≠j,k=1,2,⋯,155.


#### 3.1.2. Solving a Collection of the Shortest Path between Ports

Based on portvi to port vj judgment vector, a collection Aij of ports crossed by the shortest path between the two ports are expressed as follows:(2)Aij=vk|zkij=1,∀k,i≠j.The collection of the shortest paths between all ports can be represented by a matrix as follows:(3)A=A1−1A1−2⋯A1−155A2−1A2−2⋯A2−155⋮⋮⋱⋮A155−1A155−2⋯A155−155=∅A1−2⋯A1−155A2−1∅⋯A2−155⋮⋮⋱⋮A155−1A155−2⋯∅.


#### 3.1.3. Solving the Number of Ports Crossed by the Shortest Path

OrderXk is the total number of the shortest paths between two ports in the port network through the k port; then there is(4)Xk=∑i=1155∑j=1155zkij,j≠i,k=1,2,3,⋯,155.


### 3.2. Presentation and Analysis of Simulation Results

#### 3.2.1. Simulation Data Analysis of the Number of Ports Crossed by the Shortest Path

Based on the model in the above section, the number of crosses between ports is solved and the results are sorted from more to less, as in Table2.Table 2
The number of ports crossed by the shortest path (ports with values equal to 0 are not listed in the table; they can be searched or downloaded from the following link:https://doi.org/10.4121/14298851).
RankThe port codeName of PortThe number of ports crossed by the shortest path1v70Piraeus Port Terminal80322v35Aden Port77383v83Por Said Port74404v80Cherchell Port71865v81Suez Port69926v79Tunisia Port66367v32Jeddah66028v26Mumbai Port48429v24Colombo Port476810v68The Port of Gibraltar406411v14Singapore Port403812v102Tangier Port387213v98Dakar Port349814v144Panama City Port333815v13Penang Port332215v91Boke Terminal332217v143Colon Port324218v92Conakry Port315019v11Melaka Gateway314820v12Kuala Selangor310821v99Monrovia Port306222v130Montreal Port303823v95Abidjan Port271624v3Hong Kong260825v134Santo Domingo Port255626v49Le Havre Port212727v125New York Port211228v17Gwadar Port205829v109Sao Tome and Principe Port205030v103Dakhla Port196831v104Nouakchott Port195032v100Gentil Port189033v88Pointe Noire Port184834v89Matadi Port179235v107Walvis Port179036v113Berbera Port175437v84Luanda Port173638v34Salalah Port171239v114Cape Town Port163440v118Fremantle Port156841v96Mombasa Port155442v141San Jose Port151443v28Istanbul Port149044v66Zebrukh Port148545v30The Port of Chahbahar148046v111Dar es Saalam Port137447v29Qishm119848v135Port-au-Prince118449v133Kingston Harbor108250v115Durban Port104651v105Beira Port100852v63Port of Rotterdam94053v106Maputo Port91254v54The Kingdom of Denmark90655v20Busan89056v145Cali Port80457v4Kaohsiung Port76058v71Wado Port74059v117Melbourne Port68860v64Port of Amsterdam67261v131Havana Port64662v139Managua Port64063v18Yokohama Port63264v93Tema Port62465v53Oslo Port58866v46Hamburg Hafen56067v147Guayaquil Port55268v6Da Nang45269v86Lome Port42270v136Guatemala Port41671v37Jakarta-Kariburu37272v39Tanjung Priok36473v15Manila Port35074v132Pilon Port32875v60Murmansk Port32475v138Honduras Port32477v59Vladivostok Port31278v52Hammerforst Port30879v148Kayao Port30680v5Hanoi Port30280v33Doha Port30280v75Durres Port30283v78Varna Port30084v47London Port29685v73Reykjavík Port29486v9Laem Chabang28087v142Puerto Limon26888v119Newcastle Port24089v140Cabesas Port23490v10Kuantan Port23091v48Liverpool Port22492v23Kyaukpyu Port21692v101Cotonou Port21694v150Punta Arenas Port20895v2Guangzhou Port20296v123Manzanillo Port19497v43Nicosia Port17298v110Sudan Port17098v149San Diego Port170100v50Marseille Port154101v72San Marino Port152102v22Chattogram Port148103v67Valencia Port146103v112Tripoli Port146105v82Damietta Port132105v87Massawa Port132107v85Bata Port124108v116Darwin Port82109v8Bangkok Port66110v120Lae Port50111v7Sihanoukville8111v108Lagos Tingcan Port8113v62Sochi Port4113v94Kribi Port4115v31Dammam Port2115v40Jerusalem Port2115v42Kuwait Port2115v45Lattakia Port2115v76Constanta Port2115v137Puerto Barrios Port2In Table2, the total number of all ports crossed by the shortest path is 176,897, of which the top 17 ports, with a total of 88,949 times, accounted for 10.97% of the total number of all ports crossed by the shortest path of 50.32%; the top 23 ports, with a total of 107,177 times, accounted for 14.84% of the total number of all ports crossed by the shortest path of 60.63%; the top 31 ports, with a total of 124,614 times, accounted for 20% of the total number of all ports crossed by the shortest path of 70.49%; the top 41 ports, with a total of 141,902 times, accounted for 26.45% of the total number of all ports crossed by the shortest path of 80.26%.The simulation results show that the quantity concentration of the shortest path crossing each port is high, which meets the requirements of port network strategic pivots selection, and also show that the algorithm is effective for port network strategic pivots selection.


#### 3.2.2. Analysis of the Distribution of the Number of Ports Crossed by the Shortest Path

In order to present the simulation results more intuitively, the number of the shortest path crosses of each port is presented on the map in the form of heat attempt, and the degree of heat of the port being crossed by the shortest path is represented by thick red to light blue, and the thermal distribution results of the port are shown in Figure1.Figure 1
The thermodynamic diagram about the number of ports crossed by the shortest path.To better demonstrate the effect of the port thermal distribution, take only the first 41 ports, the sum of the number of ports crossed by the shortest path is more than 80% of the total number of ports crossed by the shortest path as shown in the thermodynamic diagram in Figure2.Figure 2
The thermodynamic diagram about rank in the top 41 of the number of ports crossed by the shortest path.As can be seen from the above two thermodynamic diagrams, most of the ports that are through are located in the channel between the major oceans, such as the Strait of Malacca between the Pacific Ocean and the Indian Ocean, the African coastline between the Indian Ocean and the Atlantic Ocean, the Red Sea Strait between the Indian Ocean and the Mediterranean Sea, the Strait of Gibraltar between the Mediterranean Sea and the Atlantic Ocean, the English Channel between the Atlantic Ocean and the North Sea, and the Panama Canal connecting the Atlantic Ocean and the Pacific Ocean.The actual situation of the port thermodynamic diagram distribution and the main international shipping paths is consistent, which shows that the basic data such as port samples, direct edge processing, and port distance data are reasonable and effective and also shows that the algorithm is feasible and effective to select the strategic pivots of the port network.


### 3.3. Analysis of the Strategic Importance of the Port

The strategic pivots of the port network are to select some ports as strategic pivots in the port network, so as to pry the development of the whole port network and promote the common economic development of the port hinterland countries and neighboring countries.According to the model solution principle of the shortest path of the network, the more times a network has been crossed by the shortest path, the closer the connection between the network and the other network outlets, the greater the role of the network, and the greater its strategic importance. Therefore, according to the number of ports crossed by the shortest path of each port in the port network, it is the standard to judge the strategic importance of the port, that is, whether the port is selected as the strategic pivot.


#### 3.3.1. Building an Analysis Model of the Strategic Importance of the Port

According to the grouping rules with similar number of ports crossed by shortest path, the K central point cluster analysis model is constructed, and the port training is divided into three groups with specific ideas:(1)
The arrayX=xi|x1,x2,⋯,x155 of the shortest path crossing each port is used as the object of machine learning and training, and xi corresponds to the number of the shortest paths crossing ports vi.(2)
Three values are found in the array with the number of centers (yj); according to the principle of the minimum difference between the values in the array and the number of centers, all the values in the number of values in the array are divided into three groups; each value is assigned to the group with the smallest difference from the number of centers; that is, all the values in the group have the closest number of crosses by the shortest path, the values xi are assigned to group j then marked xij, and xij=xi are not assigned to group j; then xij=0.(3)
Group to solve the distance between all the values of this group and the number of centers of this group, and group cumulatively adding up toY1, Y2, and Y3:(5)Yj=∑i=1155xij,j=1,2,3.(4)
Add the differences between the groups and add them up; getZ=∑j=13Yj.(5)
At the end of the training, when the sumZ value is the minimum value Zmin, the resulting grouping is the final grouping of strategic importance of the port; on this basis, according to the average size of the number of each group of ports crossed by the shortest path, the three types of ports are divided into the strategic importance “superior” group, “general” group, and “inferior” group.


#### 3.3.2. Superior Analysis and Verification of the Port Strategic Importance

According to the above grouping ideas, build an unsealed learning model; the solution results show that whenZmin= 58186, the three centers are 6992, 2050, and 296; the strategic importance of the “superior” group has 9 ports, “general” group has 39 ports, and “inferior” group has 107 ports; the specific data can be seen in Table 3.Table 3
The results of the training grouping of the number of ports crossed by the shortest path (ports in the “inferior” group are not listed; specific and available data can be searched or downloaded from the Table Port Betweenness Centrality in the following link:https://doi.org/10.4121/14298851).
Strategic importanceThe list of ports“Superior” group (9)Piraeus Port Terminal, Aden Port, Por Said Port, Cherchell Port, Suez Port, Tunisia Port, Jeddah, Mumbai Port, Colombo Port“General” group (39)The Port of Gibraltar, Singapore Port, Tangier Port, Dakar Port, Panama City Port, Yokohama port, Boke Terminal, Colon Port, Conakry Port, Melaka Gateway, Kuala Selangor, Monrovia Port, Montreal Port, Abidjan Port, Hong Kong, Santo Domingo Port, Le Havre Port, New York Port, Gwadar Port, Sao Tome and Principe Port, Dakhla Port, Nouakchott Port, Gentil Port, Pointe Noire Port, Matadi Port, Walvis Port, Berbera Port, Luanda Port, Salalah Port, Cape Town Port, Fremantle Port, Mombasa Port, San Jose Port, Istanbul Port, Zebrukh Port, the Port of Chahbahar, Dar es Saalam Port, Qishm, Port-au-PrinceFor the above training results, the grouping results were analyzed by Kruskal–Wallis test, as in Table4.Table 4
Kruskal–Wallis test grouping results.
VariableConstituenciesAverageStandard deviationThe number of samplesKruskal–Wallis inspectionThe card square valueP valueThe number of ports crossed by the shortest pathThe first group (superior)6692.891168.27921.49∗∗∗P ≤ 0.01The second group (general)2342.31847.7739The second group (general)2342.31847.773985.16∗∗∗P ≤ 0.01The third group (inferior)235.10289.84107The test results show that the variance test value is less than 0.01%, which is significant and shows that the results of strategic importance are reliable and effective.


## 3.1. Building a Model about the Number of Ports Crossed by the Shortest Path

Using the Floyd algorithm, the shortest path between two ports in the port network diagram is solved (there may be several shortest paths between the two ports, but this is not the case here, and the results simulated by Python are used as the only final result. The results of the shortest path solution can be searched or downloaded from the Table Port Shortest Path in the following link:https://doi.org/10.4121/14298851). Ports are connected only to each other, not directly to each other, and the shortest path between ports may include, in addition to the port from port to port, the passage through intermediate ports, which together with the port from the beginning constitute the shortest path from port to port. To solve the number of ports crossed by the shortest path, it needs to be solved in three steps.


### 3.1.1. Determine Whether a Port Is Crossed by a Shortest Path

Determine whether the shortest path from portvi to port vj crossed port vk or not, and remember zkij. If zkij=1, it indicates that the shortest path from port vi to port vj crossed port vk. If zkij=0, it indicates that the shortest path crossed port vk. The judgment vector for the shortest path between port vi and port vj can then be expressed as zkij, where i≠j,k=1,2,⋯,155.


### 3.1.2. Solving a Collection of the Shortest Path between Ports

Based on portvi to port vj judgment vector, a collection Aij of ports crossed by the shortest path between the two ports are expressed as follows:(2)Aij=vk|zkij=1,∀k,i≠j.The collection of the shortest paths between all ports can be represented by a matrix as follows:(3)A=A1−1A1−2⋯A1−155A2−1A2−2⋯A2−155⋮⋮⋱⋮A155−1A155−2⋯A155−155=∅A1−2⋯A1−155A2−1∅⋯A2−155⋮⋮⋱⋮A155−1A155−2⋯∅.


### 3.1.3. Solving the Number of Ports Crossed by the Shortest Path

OrderXk is the total number of the shortest paths between two ports in the port network through the k port; then there is(4)Xk=∑i=1155∑j=1155zkij,j≠i,k=1,2,3,⋯,155.


## 3.1.1. Determine Whether a Port Is Crossed by a Shortest Path

Determine whether the shortest path from portvi to port vj crossed port vk or not, and remember zkij. If zkij=1, it indicates that the shortest path from port vi to port vj crossed port vk. If zkij=0, it indicates that the shortest path crossed port vk. The judgment vector for the shortest path between port vi and port vj can then be expressed as zkij, where i≠j,k=1,2,⋯,155.


## 3.1.2. Solving a Collection of the Shortest Path between Ports

Based on portvi to port vj judgment vector, a collection Aij of ports crossed by the shortest path between the two ports are expressed as follows:(2)Aij=vk|zkij=1,∀k,i≠j.The collection of the shortest paths between all ports can be represented by a matrix as follows:(3)A=A1−1A1−2⋯A1−155A2−1A2−2⋯A2−155⋮⋮⋱⋮A155−1A155−2⋯A155−155=∅A1−2⋯A1−155A2−1∅⋯A2−155⋮⋮⋱⋮A155−1A155−2⋯∅.


## 3.1.3. Solving the Number of Ports Crossed by the Shortest Path

OrderXk is the total number of the shortest paths between two ports in the port network through the k port; then there is(4)Xk=∑i=1155∑j=1155zkij,j≠i,k=1,2,3,⋯,155.


## 3.2. Presentation and Analysis of Simulation Results

### 3.2.1. Simulation Data Analysis of the Number of Ports Crossed by the Shortest Path

Based on the model in the above section, the number of crosses between ports is solved and the results are sorted from more to less, as in Table2.Table 2
The number of ports crossed by the shortest path (ports with values equal to 0 are not listed in the table; they can be searched or downloaded from the following link:https://doi.org/10.4121/14298851).
RankThe port codeName of PortThe number of ports crossed by the shortest path1v70Piraeus Port Terminal80322v35Aden Port77383v83Por Said Port74404v80Cherchell Port71865v81Suez Port69926v79Tunisia Port66367v32Jeddah66028v26Mumbai Port48429v24Colombo Port476810v68The Port of Gibraltar406411v14Singapore Port403812v102Tangier Port387213v98Dakar Port349814v144Panama City Port333815v13Penang Port332215v91Boke Terminal332217v143Colon Port324218v92Conakry Port315019v11Melaka Gateway314820v12Kuala Selangor310821v99Monrovia Port306222v130Montreal Port303823v95Abidjan Port271624v3Hong Kong260825v134Santo Domingo Port255626v49Le Havre Port212727v125New York Port211228v17Gwadar Port205829v109Sao Tome and Principe Port205030v103Dakhla Port196831v104Nouakchott Port195032v100Gentil Port189033v88Pointe Noire Port184834v89Matadi Port179235v107Walvis Port179036v113Berbera Port175437v84Luanda Port173638v34Salalah Port171239v114Cape Town Port163440v118Fremantle Port156841v96Mombasa Port155442v141San Jose Port151443v28Istanbul Port149044v66Zebrukh Port148545v30The Port of Chahbahar148046v111Dar es Saalam Port137447v29Qishm119848v135Port-au-Prince118449v133Kingston Harbor108250v115Durban Port104651v105Beira Port100852v63Port of Rotterdam94053v106Maputo Port91254v54The Kingdom of Denmark90655v20Busan89056v145Cali Port80457v4Kaohsiung Port76058v71Wado Port74059v117Melbourne Port68860v64Port of Amsterdam67261v131Havana Port64662v139Managua Port64063v18Yokohama Port63264v93Tema Port62465v53Oslo Port58866v46Hamburg Hafen56067v147Guayaquil Port55268v6Da Nang45269v86Lome Port42270v136Guatemala Port41671v37Jakarta-Kariburu37272v39Tanjung Priok36473v15Manila Port35074v132Pilon Port32875v60Murmansk Port32475v138Honduras Port32477v59Vladivostok Port31278v52Hammerforst Port30879v148Kayao Port30680v5Hanoi Port30280v33Doha Port30280v75Durres Port30283v78Varna Port30084v47London Port29685v73Reykjavík Port29486v9Laem Chabang28087v142Puerto Limon26888v119Newcastle Port24089v140Cabesas Port23490v10Kuantan Port23091v48Liverpool Port22492v23Kyaukpyu Port21692v101Cotonou Port21694v150Punta Arenas Port20895v2Guangzhou Port20296v123Manzanillo Port19497v43Nicosia Port17298v110Sudan Port17098v149San Diego Port170100v50Marseille Port154101v72San Marino Port152102v22Chattogram Port148103v67Valencia Port146103v112Tripoli Port146105v82Damietta Port132105v87Massawa Port132107v85Bata Port124108v116Darwin Port82109v8Bangkok Port66110v120Lae Port50111v7Sihanoukville8111v108Lagos Tingcan Port8113v62Sochi Port4113v94Kribi Port4115v31Dammam Port2115v40Jerusalem Port2115v42Kuwait Port2115v45Lattakia Port2115v76Constanta Port2115v137Puerto Barrios Port2In Table2, the total number of all ports crossed by the shortest path is 176,897, of which the top 17 ports, with a total of 88,949 times, accounted for 10.97% of the total number of all ports crossed by the shortest path of 50.32%; the top 23 ports, with a total of 107,177 times, accounted for 14.84% of the total number of all ports crossed by the shortest path of 60.63%; the top 31 ports, with a total of 124,614 times, accounted for 20% of the total number of all ports crossed by the shortest path of 70.49%; the top 41 ports, with a total of 141,902 times, accounted for 26.45% of the total number of all ports crossed by the shortest path of 80.26%.The simulation results show that the quantity concentration of the shortest path crossing each port is high, which meets the requirements of port network strategic pivots selection, and also show that the algorithm is effective for port network strategic pivots selection.


### 3.2.2. Analysis of the Distribution of the Number of Ports Crossed by the Shortest Path

In order to present the simulation results more intuitively, the number of the shortest path crosses of each port is presented on the map in the form of heat attempt, and the degree of heat of the port being crossed by the shortest path is represented by thick red to light blue, and the thermal distribution results of the port are shown in Figure1.Figure 1
The thermodynamic diagram about the number of ports crossed by the shortest path.To better demonstrate the effect of the port thermal distribution, take only the first 41 ports, the sum of the number of ports crossed by the shortest path is more than 80% of the total number of ports crossed by the shortest path as shown in the thermodynamic diagram in Figure2.Figure 2
The thermodynamic diagram about rank in the top 41 of the number of ports crossed by the shortest path.As can be seen from the above two thermodynamic diagrams, most of the ports that are through are located in the channel between the major oceans, such as the Strait of Malacca between the Pacific Ocean and the Indian Ocean, the African coastline between the Indian Ocean and the Atlantic Ocean, the Red Sea Strait between the Indian Ocean and the Mediterranean Sea, the Strait of Gibraltar between the Mediterranean Sea and the Atlantic Ocean, the English Channel between the Atlantic Ocean and the North Sea, and the Panama Canal connecting the Atlantic Ocean and the Pacific Ocean.The actual situation of the port thermodynamic diagram distribution and the main international shipping paths is consistent, which shows that the basic data such as port samples, direct edge processing, and port distance data are reasonable and effective and also shows that the algorithm is feasible and effective to select the strategic pivots of the port network.


## 3.2.1. Simulation Data Analysis of the Number of Ports Crossed by the Shortest Path

Based on the model in the above section, the number of crosses between ports is solved and the results are sorted from more to less, as in Table2.Table 2
The number of ports crossed by the shortest path (ports with values equal to 0 are not listed in the table; they can be searched or downloaded from the following link:https://doi.org/10.4121/14298851).
RankThe port codeName of PortThe number of ports crossed by the shortest path1v70Piraeus Port Terminal80322v35Aden Port77383v83Por Said Port74404v80Cherchell Port71865v81Suez Port69926v79Tunisia Port66367v32Jeddah66028v26Mumbai Port48429v24Colombo Port476810v68The Port of Gibraltar406411v14Singapore Port403812v102Tangier Port387213v98Dakar Port349814v144Panama City Port333815v13Penang Port332215v91Boke Terminal332217v143Colon Port324218v92Conakry Port315019v11Melaka Gateway314820v12Kuala Selangor310821v99Monrovia Port306222v130Montreal Port303823v95Abidjan Port271624v3Hong Kong260825v134Santo Domingo Port255626v49Le Havre Port212727v125New York Port211228v17Gwadar Port205829v109Sao Tome and Principe Port205030v103Dakhla Port196831v104Nouakchott Port195032v100Gentil Port189033v88Pointe Noire Port184834v89Matadi Port179235v107Walvis Port179036v113Berbera Port175437v84Luanda Port173638v34Salalah Port171239v114Cape Town Port163440v118Fremantle Port156841v96Mombasa Port155442v141San Jose Port151443v28Istanbul Port149044v66Zebrukh Port148545v30The Port of Chahbahar148046v111Dar es Saalam Port137447v29Qishm119848v135Port-au-Prince118449v133Kingston Harbor108250v115Durban Port104651v105Beira Port100852v63Port of Rotterdam94053v106Maputo Port91254v54The Kingdom of Denmark90655v20Busan89056v145Cali Port80457v4Kaohsiung Port76058v71Wado Port74059v117Melbourne Port68860v64Port of Amsterdam67261v131Havana Port64662v139Managua Port64063v18Yokohama Port63264v93Tema Port62465v53Oslo Port58866v46Hamburg Hafen56067v147Guayaquil Port55268v6Da Nang45269v86Lome Port42270v136Guatemala Port41671v37Jakarta-Kariburu37272v39Tanjung Priok36473v15Manila Port35074v132Pilon Port32875v60Murmansk Port32475v138Honduras Port32477v59Vladivostok Port31278v52Hammerforst Port30879v148Kayao Port30680v5Hanoi Port30280v33Doha Port30280v75Durres Port30283v78Varna Port30084v47London Port29685v73Reykjavík Port29486v9Laem Chabang28087v142Puerto Limon26888v119Newcastle Port24089v140Cabesas Port23490v10Kuantan Port23091v48Liverpool Port22492v23Kyaukpyu Port21692v101Cotonou Port21694v150Punta Arenas Port20895v2Guangzhou Port20296v123Manzanillo Port19497v43Nicosia Port17298v110Sudan Port17098v149San Diego Port170100v50Marseille Port154101v72San Marino Port152102v22Chattogram Port148103v67Valencia Port146103v112Tripoli Port146105v82Damietta Port132105v87Massawa Port132107v85Bata Port124108v116Darwin Port82109v8Bangkok Port66110v120Lae Port50111v7Sihanoukville8111v108Lagos Tingcan Port8113v62Sochi Port4113v94Kribi Port4115v31Dammam Port2115v40Jerusalem Port2115v42Kuwait Port2115v45Lattakia Port2115v76Constanta Port2115v137Puerto Barrios Port2In Table2, the total number of all ports crossed by the shortest path is 176,897, of which the top 17 ports, with a total of 88,949 times, accounted for 10.97% of the total number of all ports crossed by the shortest path of 50.32%; the top 23 ports, with a total of 107,177 times, accounted for 14.84% of the total number of all ports crossed by the shortest path of 60.63%; the top 31 ports, with a total of 124,614 times, accounted for 20% of the total number of all ports crossed by the shortest path of 70.49%; the top 41 ports, with a total of 141,902 times, accounted for 26.45% of the total number of all ports crossed by the shortest path of 80.26%.The simulation results show that the quantity concentration of the shortest path crossing each port is high, which meets the requirements of port network strategic pivots selection, and also show that the algorithm is effective for port network strategic pivots selection.


## 3.2.2. Analysis of the Distribution of the Number of Ports Crossed by the Shortest Path

In order to present the simulation results more intuitively, the number of the shortest path crosses of each port is presented on the map in the form of heat attempt, and the degree of heat of the port being crossed by the shortest path is represented by thick red to light blue, and the thermal distribution results of the port are shown in Figure1.Figure 1
The thermodynamic diagram about the number of ports crossed by the shortest path.To better demonstrate the effect of the port thermal distribution, take only the first 41 ports, the sum of the number of ports crossed by the shortest path is more than 80% of the total number of ports crossed by the shortest path as shown in the thermodynamic diagram in Figure2.Figure 2
The thermodynamic diagram about rank in the top 41 of the number of ports crossed by the shortest path.As can be seen from the above two thermodynamic diagrams, most of the ports that are through are located in the channel between the major oceans, such as the Strait of Malacca between the Pacific Ocean and the Indian Ocean, the African coastline between the Indian Ocean and the Atlantic Ocean, the Red Sea Strait between the Indian Ocean and the Mediterranean Sea, the Strait of Gibraltar between the Mediterranean Sea and the Atlantic Ocean, the English Channel between the Atlantic Ocean and the North Sea, and the Panama Canal connecting the Atlantic Ocean and the Pacific Ocean.The actual situation of the port thermodynamic diagram distribution and the main international shipping paths is consistent, which shows that the basic data such as port samples, direct edge processing, and port distance data are reasonable and effective and also shows that the algorithm is feasible and effective to select the strategic pivots of the port network.


## 3.3. Analysis of the Strategic Importance of the Port

The strategic pivots of the port network are to select some ports as strategic pivots in the port network, so as to pry the development of the whole port network and promote the common economic development of the port hinterland countries and neighboring countries.According to the model solution principle of the shortest path of the network, the more times a network has been crossed by the shortest path, the closer the connection between the network and the other network outlets, the greater the role of the network, and the greater its strategic importance. Therefore, according to the number of ports crossed by the shortest path of each port in the port network, it is the standard to judge the strategic importance of the port, that is, whether the port is selected as the strategic pivot.


### 3.3.1. Building an Analysis Model of the Strategic Importance of the Port

According to the grouping rules with similar number of ports crossed by shortest path, the K central point cluster analysis model is constructed, and the port training is divided into three groups with specific ideas:(1)
The arrayX=xi|x1,x2,⋯,x155 of the shortest path crossing each port is used as the object of machine learning and training, and xi corresponds to the number of the shortest paths crossing ports vi.(2)
Three values are found in the array with the number of centers (yj); according to the principle of the minimum difference between the values in the array and the number of centers, all the values in the number of values in the array are divided into three groups; each value is assigned to the group with the smallest difference from the number of centers; that is, all the values in the group have the closest number of crosses by the shortest path, the values xi are assigned to group j then marked xij, and xij=xi are not assigned to group j; then xij=0.(3)
Group to solve the distance between all the values of this group and the number of centers of this group, and group cumulatively adding up toY1, Y2, and Y3:(5)Yj=∑i=1155xij,j=1,2,3.(4)
Add the differences between the groups and add them up; getZ=∑j=13Yj.(5)
At the end of the training, when the sumZ value is the minimum value Zmin, the resulting grouping is the final grouping of strategic importance of the port; on this basis, according to the average size of the number of each group of ports crossed by the shortest path, the three types of ports are divided into the strategic importance “superior” group, “general” group, and “inferior” group.


### 3.3.2. Superior Analysis and Verification of the Port Strategic Importance

According to the above grouping ideas, build an unsealed learning model; the solution results show that whenZmin= 58186, the three centers are 6992, 2050, and 296; the strategic importance of the “superior” group has 9 ports, “general” group has 39 ports, and “inferior” group has 107 ports; the specific data can be seen in Table 3.Table 3
The results of the training grouping of the number of ports crossed by the shortest path (ports in the “inferior” group are not listed; specific and available data can be searched or downloaded from the Table Port Betweenness Centrality in the following link:https://doi.org/10.4121/14298851).
Strategic importanceThe list of ports“Superior” group (9)Piraeus Port Terminal, Aden Port, Por Said Port, Cherchell Port, Suez Port, Tunisia Port, Jeddah, Mumbai Port, Colombo Port“General” group (39)The Port of Gibraltar, Singapore Port, Tangier Port, Dakar Port, Panama City Port, Yokohama port, Boke Terminal, Colon Port, Conakry Port, Melaka Gateway, Kuala Selangor, Monrovia Port, Montreal Port, Abidjan Port, Hong Kong, Santo Domingo Port, Le Havre Port, New York Port, Gwadar Port, Sao Tome and Principe Port, Dakhla Port, Nouakchott Port, Gentil Port, Pointe Noire Port, Matadi Port, Walvis Port, Berbera Port, Luanda Port, Salalah Port, Cape Town Port, Fremantle Port, Mombasa Port, San Jose Port, Istanbul Port, Zebrukh Port, the Port of Chahbahar, Dar es Saalam Port, Qishm, Port-au-PrinceFor the above training results, the grouping results were analyzed by Kruskal–Wallis test, as in Table4.Table 4
Kruskal–Wallis test grouping results.
VariableConstituenciesAverageStandard deviationThe number of samplesKruskal–Wallis inspectionThe card square valueP valueThe number of ports crossed by the shortest pathThe first group (superior)6692.891168.27921.49∗∗∗P ≤ 0.01The second group (general)2342.31847.7739The second group (general)2342.31847.773985.16∗∗∗P ≤ 0.01The third group (inferior)235.10289.84107The test results show that the variance test value is less than 0.01%, which is significant and shows that the results of strategic importance are reliable and effective.


## 3.3.1. Building an Analysis Model of the Strategic Importance of the Port

According to the grouping rules with similar number of ports crossed by shortest path, the K central point cluster analysis model is constructed, and the port training is divided into three groups with specific ideas:(1)
The arrayX=xi|x1,x2,⋯,x155 of the shortest path crossing each port is used as the object of machine learning and training, and xi corresponds to the number of the shortest paths crossing ports vi.(2)
Three values are found in the array with the number of centers (yj); according to the principle of the minimum difference between the values in the array and the number of centers, all the values in the number of values in the array are divided into three groups; each value is assigned to the group with the smallest difference from the number of centers; that is, all the values in the group have the closest number of crosses by the shortest path, the values xi are assigned to group j then marked xij, and xij=xi are not assigned to group j; then xij=0.(3)
Group to solve the distance between all the values of this group and the number of centers of this group, and group cumulatively adding up toY1, Y2, and Y3:(5)Yj=∑i=1155xij,j=1,2,3.(4)
Add the differences between the groups and add them up; getZ=∑j=13Yj.(5)
At the end of the training, when the sumZ value is the minimum value Zmin, the resulting grouping is the final grouping of strategic importance of the port; on this basis, according to the average size of the number of each group of ports crossed by the shortest path, the three types of ports are divided into the strategic importance “superior” group, “general” group, and “inferior” group.


## 3.3.2. Superior Analysis and Verification of the Port Strategic Importance

According to the above grouping ideas, build an unsealed learning model; the solution results show that whenZmin= 58186, the three centers are 6992, 2050, and 296; the strategic importance of the “superior” group has 9 ports, “general” group has 39 ports, and “inferior” group has 107 ports; the specific data can be seen in Table 3.Table 3
The results of the training grouping of the number of ports crossed by the shortest path (ports in the “inferior” group are not listed; specific and available data can be searched or downloaded from the Table Port Betweenness Centrality in the following link:https://doi.org/10.4121/14298851).
Strategic importanceThe list of ports“Superior” group (9)Piraeus Port Terminal, Aden Port, Por Said Port, Cherchell Port, Suez Port, Tunisia Port, Jeddah, Mumbai Port, Colombo Port“General” group (39)The Port of Gibraltar, Singapore Port, Tangier Port, Dakar Port, Panama City Port, Yokohama port, Boke Terminal, Colon Port, Conakry Port, Melaka Gateway, Kuala Selangor, Monrovia Port, Montreal Port, Abidjan Port, Hong Kong, Santo Domingo Port, Le Havre Port, New York Port, Gwadar Port, Sao Tome and Principe Port, Dakhla Port, Nouakchott Port, Gentil Port, Pointe Noire Port, Matadi Port, Walvis Port, Berbera Port, Luanda Port, Salalah Port, Cape Town Port, Fremantle Port, Mombasa Port, San Jose Port, Istanbul Port, Zebrukh Port, the Port of Chahbahar, Dar es Saalam Port, Qishm, Port-au-PrinceFor the above training results, the grouping results were analyzed by Kruskal–Wallis test, as in Table4.Table 4
Kruskal–Wallis test grouping results.
VariableConstituenciesAverageStandard deviationThe number of samplesKruskal–Wallis inspectionThe card square valueP valueThe number of ports crossed by the shortest pathThe first group (superior)6692.891168.27921.49∗∗∗P ≤ 0.01The second group (general)2342.31847.7739The second group (general)2342.31847.773985.16∗∗∗P ≤ 0.01The third group (inferior)235.10289.84107The test results show that the variance test value is less than 0.01%, which is significant and shows that the results of strategic importance are reliable and effective.


## 4. Strategic Pivots Selection Based on Betweenness Centrality of the Port Network

Betweenness centrality is one of the measures of network vertexes to network graph centrality. For the whole port network, the greater the value of the betweenness centrality of the port is, the greater the influence and control of the port on the entire port network are, the stronger its strategic importance is, and the more the port should be preferred as the strategic pivots port of the entire network.


### 4.1. Building a Strategically Important Model of Port Network

According to the principle of betweenness centrality model, the numberQijk of port vk through the shortest path between port vi and port vj in the whole network, and the ratio of the total number Qij of shortest paths between port vi and port vj, the sum of the ratios throughout the network is as follows:(6)BCk=∑i≠j≠k∈NQijkQij.That is the betweenness centrality of the port.


### 4.2. Presentation and Analysis of Simulation Results

To be comparable, the underlying data and settings in this section are the same as in the previous section.


#### 4.2.1. Analysis of Betweenness Centrality Values

According to the betweenness centrality model, the betweenness centrality of each port is solved and the results are sorted, as in Table5.Table 5
The betweenness centrality for each port.
The port codePortBetweenness centralityv118Fremantle Port6431.97v35Aden Port5826.28v14Singapore Port5088.82v144Panama City Port4863.39v125New York Port4716.63v114Cape Town Port4706.16v143Colon Port4501.09v3Hong Kong4325.15v104Nouakchott Port3762.52v154Santos Port3721.93v70Piraeus Port Terminal3403.56v80Cherchell Port3346.09v83Por Said Port2850.96v32Jeddah2547.05v81Suez Port2532.32v134Santo Domingo Port2371.64v68The Port of Gibraltar2170.51v107Walvis Port2156.25v26Mumbai Port2135.30v17Gwadar Port2059v109Sao Tome and Principe Port1956.94v24Colombo Port1862.11v102Tangier Port1858.771v130Montreal Port1839.79v71Wado Port1558.43v37Jakarta-Kariburu1515.73v28Istanbul Port1492v79Tunisia Port1479.56v150Punta Arenas Port1458.78v140Cabesas Port1427.31v132Pilon port1356.69v47London Port1351.42v18Yokohama Port1254.07v39Tanjung Priok1235.17v16Abu Dhabi Port1085.33v54The Kingdom of Denmark1083.86v99Monrovia Port1076.67v1Shanghai Port1074.54v34Salalah Port1073.07v115Durban Port1047.97v135Port-au-Prince836.05v131Havana Port782.24v155St Louis Port757.51v152Buenos Aires Port674.36v49Le Havre Port570.08v48Liverpool Port554.59v66Zebrukh Port530.32v153Paranagua Port515.64v29Qishm506v113Berbera Port432.03v116Darwin Port414.89v98Dakar Port405.60v33Doha Port400.67v30The Port of Chahbahar394.67v59Vladivostok Port381.27v117Melbourne Port375.67v141San Jose Port370.95v60Murmansk Port369.73v145Cali Port359.73v12Kuala Selangor347.00v2Guangzhou Port320.10v149San Diego Port318.28v75Durres Port299.52v97Tamataf Port295.74v88Pointe Noire Port272.74v96Mombasa Port255.33v111Dar es Saalam Port253.41v106Maputo Port216.67v20Busan212.17v119Newcastle Port210.52v84Luanda Port201.06v13Penang Port193.72v147Guayaquil Port173.53v8Bangkok Port172.66v53Oslo Port170.08v103Dakhla Port161.42v133Kingston Harbor151.63v148Kayao Port151.39v4Kaohsiung Port147.902v95Abidjan Port137.31v112Tripoli Port136.92v151La Guaira Port134.38v91Boke Terminal133.99v11Melaka Gateway129.34v92Conakry Port117.8v90Djibouti Port111.56v82Damietta Port102.8v15Manila Port100.04v87Masawa Port91.45v5Hanoi Port89.57v6Da Nang87.97v62Sochi Port77v64Port of Amsterdam75.59v41Batumi Port75v77Odessa Port75v78Varna Port75v128Vancouver Port72.38v43Nicosia Port64.60v72San Marino Port61.73v138Honduras Port58.97v121Wellington Port55.77v7Sihanoukville49.75v10Kuantan Port49.75v67Valencia Port46.27v50Marseille Port44.04v46Hamburg Hafen38.64v129Churchill Port34.24v110Sudan Port33.85v146Barranquilla Port29.047v142Puerto limon28.57v73Reykjavík Port23.04v127New Orleans Port22.08v100Gentil Port11.41v124Veracruz Port7.36v137Puerto Barrios Port7.36v63Port of Rotterdam5.33v120Lae Port3.83v122Suva Port3.83v105Beira Port3.67v9Laem Chabang3v42Kuwait Port3v89Matadi Port2.75v93Tema Port2.67v52Hammerforst Port2.57v38Jambi International Port2.33v22Chattogram Port2v27Chennai Port2v76Constanta Port2v85Bata Port1.83v123Manzanillo Port1.79v139Managua Port1.79v126Port of Long Beach, Los Angeles1.186v23Kyaukpyu Port1v40Jerusalem Port1v45Lattakia Port1v86Lome Port1v94Kribi Port1v101Cotonou Port1v108Lagos Tingcan Port1v136Guatemala Port0.79v31Dammam Port0.67v44Basrah Port0.67v19Chongjin Port0In the table above, the sum of the betweenness centralities of all ports is 118306, of which, for the top 14 ports, the sum of their betweenness centralities is 60091.60, and 9.03% of the port number accounts for 50.79% of the betweenness centrality sum; for the top 19 ports, the sum of their betweenness centralities is 71457.63, and 12.26% of the port number accounts for 60.4% of the betweenness centrality sum; for the top 26 ports, the sum of their betweenness centralities is 84108.40, and 16.77% of the port number accounts for 71.09% of the betweenness centrality sum; for the top 34 ports, the sum of their betweenness centralities is 95163.40, and 21.94% of the port number accounts for 80.44% of the betweenness centrality sum. The simulation results show that the centralization of the port is high, and, from the point of view of the concentration of the betweenness centrality, the simulation results meet the requirements of the port strategy pivots selection, and they also show that it is effective in judging the strategic importance of the port in the whole network based on the betweenness centrality.


#### 4.2.2. Analysis of Betweenness Centrality Distribution Map

In order to present the simulation results more intuitively, the betweenness centrality of each port is presented on the map in the form of heat-trying, and the degree of the betweenness centrality of the port is represented by thick red to light blue, and the distribution results of the port thermal force are shown in Figure3.Figure 3
The thermodynamic diagram about the betweenness centrality of each port.In order to better demonstrate the distribution effect of port betweenness centrality heat, only the top 34 are shown, and the sum of betweenness centralities exceeds 80% of the port heating, as shown in Figure4.Figure 4
The thermodynamic diagram about rank in the top 34 ports in the betweenness centrality.From the above two thermal distribution charts, it can be seen that most of the ports with large betweenness centrality values are distributed in the channels between the major oceans; it can be seen that the distribution of port betweenness centrality heat is consistent with the actual situation of the major international shipping paths, indicating that the basic data such as port samples, direct edge processing, and port distance data are reasonable and effective and that the algorithm is feasible and effective to carry out strategic pivots analysis of the port network.


### 4.3. Superior Analysis and Verification of the Port Strategic Importance

According to the model solution principle of betweenness centrality, the greater the betweenness centrality value of a dot in the network, which indicates closer connection between the dot and other networks in the network, the greater the influence, the greater the role played on the network, and the greater the strategic importance.According to the third part of the clustering algorithm, the training results show that when the three sets of data differenceZmin = 35688.46, the three centers are 4706.16, 1479.56, and 61.73; the strategic importance of the “superior” group has 12 ports, “general” group has 30 ports, and “inferior” group has 113 ports, as in Table 6.Table 6
Group results by interstitial central numerical training (ports in the “inferior” group are not listed; specific and available data can be searched or downloaded from the Table Port Betweenness Centrality in the following link:https://doi.org/10.4121/14298851).
Strategic importanceThe list of ports“Superior” group (12)Fremantle Port, Aden Port, Singapore Port, Panama City Port, New York Port, Cape Town Port, Colon Port, Hong Kong, Nouakchott Port, Santos Port, Piraeus Port Terminal, Cherchell Port“General” group (30)Por Said Port, Jeddah, Suez Port, Santo Domingo Port, the Port of Gibraltar, Walvis Port, Mumbai Port, Gwadar Port, Sao Tome and Principe Port, Colombo Port, Tangier Port, Montreal Port, Wado Port, Jakarta-Kariburu, Istanbul Port, Tunisia Port, Punta Arenas Port, Cabesas Port, Pilon Port, London Port, Yokohama Port, Tanjung Priok, Abu Dhabi Port, the Kingdom of Denmark, Monrovia Port, Shanghai Port, Salalah Port, Durban Port, Port-au-Prince, Havana PortFor the above training results, the grouping results were analyzed by Kruskal–Wallis test, as in Table7.Table 7
Kruskal–Wallis test grouping results.
VariableConstituenciesAverageStandard deviationThe number of samplesKruskal–Wallis inspectionThe card square valueP valueThe number of ports crossed by the shortest pathThe first group (superior)4557.80940.661225.12∗∗∗P ≤ 0.01The second group (general)1617.6554.1230The second group (general)1617.6554.123070.63∗∗∗P ≤ 0.01The third group (inferior)133.48171.87113According to the above test results, the average variance of the three sets of data is less than 0.01%.


## 4.1. Building a Strategically Important Model of Port Network

According to the principle of betweenness centrality model, the numberQijk of port vk through the shortest path between port vi and port vj in the whole network, and the ratio of the total number Qij of shortest paths between port vi and port vj, the sum of the ratios throughout the network is as follows:(6)BCk=∑i≠j≠k∈NQijkQij.That is the betweenness centrality of the port.


## 4.2. Presentation and Analysis of Simulation Results

To be comparable, the underlying data and settings in this section are the same as in the previous section.


### 4.2.1. Analysis of Betweenness Centrality Values

According to the betweenness centrality model, the betweenness centrality of each port is solved and the results are sorted, as in Table5.Table 5
The betweenness centrality for each port.
The port codePortBetweenness centralityv118Fremantle Port6431.97v35Aden Port5826.28v14Singapore Port5088.82v144Panama City Port4863.39v125New York Port4716.63v114Cape Town Port4706.16v143Colon Port4501.09v3Hong Kong4325.15v104Nouakchott Port3762.52v154Santos Port3721.93v70Piraeus Port Terminal3403.56v80Cherchell Port3346.09v83Por Said Port2850.96v32Jeddah2547.05v81Suez Port2532.32v134Santo Domingo Port2371.64v68The Port of Gibraltar2170.51v107Walvis Port2156.25v26Mumbai Port2135.30v17Gwadar Port2059v109Sao Tome and Principe Port1956.94v24Colombo Port1862.11v102Tangier Port1858.771v130Montreal Port1839.79v71Wado Port1558.43v37Jakarta-Kariburu1515.73v28Istanbul Port1492v79Tunisia Port1479.56v150Punta Arenas Port1458.78v140Cabesas Port1427.31v132Pilon port1356.69v47London Port1351.42v18Yokohama Port1254.07v39Tanjung Priok1235.17v16Abu Dhabi Port1085.33v54The Kingdom of Denmark1083.86v99Monrovia Port1076.67v1Shanghai Port1074.54v34Salalah Port1073.07v115Durban Port1047.97v135Port-au-Prince836.05v131Havana Port782.24v155St Louis Port757.51v152Buenos Aires Port674.36v49Le Havre Port570.08v48Liverpool Port554.59v66Zebrukh Port530.32v153Paranagua Port515.64v29Qishm506v113Berbera Port432.03v116Darwin Port414.89v98Dakar Port405.60v33Doha Port400.67v30The Port of Chahbahar394.67v59Vladivostok Port381.27v117Melbourne Port375.67v141San Jose Port370.95v60Murmansk Port369.73v145Cali Port359.73v12Kuala Selangor347.00v2Guangzhou Port320.10v149San Diego Port318.28v75Durres Port299.52v97Tamataf Port295.74v88Pointe Noire Port272.74v96Mombasa Port255.33v111Dar es Saalam Port253.41v106Maputo Port216.67v20Busan212.17v119Newcastle Port210.52v84Luanda Port201.06v13Penang Port193.72v147Guayaquil Port173.53v8Bangkok Port172.66v53Oslo Port170.08v103Dakhla Port161.42v133Kingston Harbor151.63v148Kayao Port151.39v4Kaohsiung Port147.902v95Abidjan Port137.31v112Tripoli Port136.92v151La Guaira Port134.38v91Boke Terminal133.99v11Melaka Gateway129.34v92Conakry Port117.8v90Djibouti Port111.56v82Damietta Port102.8v15Manila Port100.04v87Masawa Port91.45v5Hanoi Port89.57v6Da Nang87.97v62Sochi Port77v64Port of Amsterdam75.59v41Batumi Port75v77Odessa Port75v78Varna Port75v128Vancouver Port72.38v43Nicosia Port64.60v72San Marino Port61.73v138Honduras Port58.97v121Wellington Port55.77v7Sihanoukville49.75v10Kuantan Port49.75v67Valencia Port46.27v50Marseille Port44.04v46Hamburg Hafen38.64v129Churchill Port34.24v110Sudan Port33.85v146Barranquilla Port29.047v142Puerto limon28.57v73Reykjavík Port23.04v127New Orleans Port22.08v100Gentil Port11.41v124Veracruz Port7.36v137Puerto Barrios Port7.36v63Port of Rotterdam5.33v120Lae Port3.83v122Suva Port3.83v105Beira Port3.67v9Laem Chabang3v42Kuwait Port3v89Matadi Port2.75v93Tema Port2.67v52Hammerforst Port2.57v38Jambi International Port2.33v22Chattogram Port2v27Chennai Port2v76Constanta Port2v85Bata Port1.83v123Manzanillo Port1.79v139Managua Port1.79v126Port of Long Beach, Los Angeles1.186v23Kyaukpyu Port1v40Jerusalem Port1v45Lattakia Port1v86Lome Port1v94Kribi Port1v101Cotonou Port1v108Lagos Tingcan Port1v136Guatemala Port0.79v31Dammam Port0.67v44Basrah Port0.67v19Chongjin Port0In the table above, the sum of the betweenness centralities of all ports is 118306, of which, for the top 14 ports, the sum of their betweenness centralities is 60091.60, and 9.03% of the port number accounts for 50.79% of the betweenness centrality sum; for the top 19 ports, the sum of their betweenness centralities is 71457.63, and 12.26% of the port number accounts for 60.4% of the betweenness centrality sum; for the top 26 ports, the sum of their betweenness centralities is 84108.40, and 16.77% of the port number accounts for 71.09% of the betweenness centrality sum; for the top 34 ports, the sum of their betweenness centralities is 95163.40, and 21.94% of the port number accounts for 80.44% of the betweenness centrality sum. The simulation results show that the centralization of the port is high, and, from the point of view of the concentration of the betweenness centrality, the simulation results meet the requirements of the port strategy pivots selection, and they also show that it is effective in judging the strategic importance of the port in the whole network based on the betweenness centrality.


### 4.2.2. Analysis of Betweenness Centrality Distribution Map

In order to present the simulation results more intuitively, the betweenness centrality of each port is presented on the map in the form of heat-trying, and the degree of the betweenness centrality of the port is represented by thick red to light blue, and the distribution results of the port thermal force are shown in Figure3.Figure 3
The thermodynamic diagram about the betweenness centrality of each port.In order to better demonstrate the distribution effect of port betweenness centrality heat, only the top 34 are shown, and the sum of betweenness centralities exceeds 80% of the port heating, as shown in Figure4.Figure 4
The thermodynamic diagram about rank in the top 34 ports in the betweenness centrality.From the above two thermal distribution charts, it can be seen that most of the ports with large betweenness centrality values are distributed in the channels between the major oceans; it can be seen that the distribution of port betweenness centrality heat is consistent with the actual situation of the major international shipping paths, indicating that the basic data such as port samples, direct edge processing, and port distance data are reasonable and effective and that the algorithm is feasible and effective to carry out strategic pivots analysis of the port network.


## 4.2.1. Analysis of Betweenness Centrality Values

According to the betweenness centrality model, the betweenness centrality of each port is solved and the results are sorted, as in Table5.Table 5
The betweenness centrality for each port.
The port codePortBetweenness centralityv118Fremantle Port6431.97v35Aden Port5826.28v14Singapore Port5088.82v144Panama City Port4863.39v125New York Port4716.63v114Cape Town Port4706.16v143Colon Port4501.09v3Hong Kong4325.15v104Nouakchott Port3762.52v154Santos Port3721.93v70Piraeus Port Terminal3403.56v80Cherchell Port3346.09v83Por Said Port2850.96v32Jeddah2547.05v81Suez Port2532.32v134Santo Domingo Port2371.64v68The Port of Gibraltar2170.51v107Walvis Port2156.25v26Mumbai Port2135.30v17Gwadar Port2059v109Sao Tome and Principe Port1956.94v24Colombo Port1862.11v102Tangier Port1858.771v130Montreal Port1839.79v71Wado Port1558.43v37Jakarta-Kariburu1515.73v28Istanbul Port1492v79Tunisia Port1479.56v150Punta Arenas Port1458.78v140Cabesas Port1427.31v132Pilon port1356.69v47London Port1351.42v18Yokohama Port1254.07v39Tanjung Priok1235.17v16Abu Dhabi Port1085.33v54The Kingdom of Denmark1083.86v99Monrovia Port1076.67v1Shanghai Port1074.54v34Salalah Port1073.07v115Durban Port1047.97v135Port-au-Prince836.05v131Havana Port782.24v155St Louis Port757.51v152Buenos Aires Port674.36v49Le Havre Port570.08v48Liverpool Port554.59v66Zebrukh Port530.32v153Paranagua Port515.64v29Qishm506v113Berbera Port432.03v116Darwin Port414.89v98Dakar Port405.60v33Doha Port400.67v30The Port of Chahbahar394.67v59Vladivostok Port381.27v117Melbourne Port375.67v141San Jose Port370.95v60Murmansk Port369.73v145Cali Port359.73v12Kuala Selangor347.00v2Guangzhou Port320.10v149San Diego Port318.28v75Durres Port299.52v97Tamataf Port295.74v88Pointe Noire Port272.74v96Mombasa Port255.33v111Dar es Saalam Port253.41v106Maputo Port216.67v20Busan212.17v119Newcastle Port210.52v84Luanda Port201.06v13Penang Port193.72v147Guayaquil Port173.53v8Bangkok Port172.66v53Oslo Port170.08v103Dakhla Port161.42v133Kingston Harbor151.63v148Kayao Port151.39v4Kaohsiung Port147.902v95Abidjan Port137.31v112Tripoli Port136.92v151La Guaira Port134.38v91Boke Terminal133.99v11Melaka Gateway129.34v92Conakry Port117.8v90Djibouti Port111.56v82Damietta Port102.8v15Manila Port100.04v87Masawa Port91.45v5Hanoi Port89.57v6Da Nang87.97v62Sochi Port77v64Port of Amsterdam75.59v41Batumi Port75v77Odessa Port75v78Varna Port75v128Vancouver Port72.38v43Nicosia Port64.60v72San Marino Port61.73v138Honduras Port58.97v121Wellington Port55.77v7Sihanoukville49.75v10Kuantan Port49.75v67Valencia Port46.27v50Marseille Port44.04v46Hamburg Hafen38.64v129Churchill Port34.24v110Sudan Port33.85v146Barranquilla Port29.047v142Puerto limon28.57v73Reykjavík Port23.04v127New Orleans Port22.08v100Gentil Port11.41v124Veracruz Port7.36v137Puerto Barrios Port7.36v63Port of Rotterdam5.33v120Lae Port3.83v122Suva Port3.83v105Beira Port3.67v9Laem Chabang3v42Kuwait Port3v89Matadi Port2.75v93Tema Port2.67v52Hammerforst Port2.57v38Jambi International Port2.33v22Chattogram Port2v27Chennai Port2v76Constanta Port2v85Bata Port1.83v123Manzanillo Port1.79v139Managua Port1.79v126Port of Long Beach, Los Angeles1.186v23Kyaukpyu Port1v40Jerusalem Port1v45Lattakia Port1v86Lome Port1v94Kribi Port1v101Cotonou Port1v108Lagos Tingcan Port1v136Guatemala Port0.79v31Dammam Port0.67v44Basrah Port0.67v19Chongjin Port0In the table above, the sum of the betweenness centralities of all ports is 118306, of which, for the top 14 ports, the sum of their betweenness centralities is 60091.60, and 9.03% of the port number accounts for 50.79% of the betweenness centrality sum; for the top 19 ports, the sum of their betweenness centralities is 71457.63, and 12.26% of the port number accounts for 60.4% of the betweenness centrality sum; for the top 26 ports, the sum of their betweenness centralities is 84108.40, and 16.77% of the port number accounts for 71.09% of the betweenness centrality sum; for the top 34 ports, the sum of their betweenness centralities is 95163.40, and 21.94% of the port number accounts for 80.44% of the betweenness centrality sum. The simulation results show that the centralization of the port is high, and, from the point of view of the concentration of the betweenness centrality, the simulation results meet the requirements of the port strategy pivots selection, and they also show that it is effective in judging the strategic importance of the port in the whole network based on the betweenness centrality.


## 4.2.2. Analysis of Betweenness Centrality Distribution Map

In order to present the simulation results more intuitively, the betweenness centrality of each port is presented on the map in the form of heat-trying, and the degree of the betweenness centrality of the port is represented by thick red to light blue, and the distribution results of the port thermal force are shown in Figure3.Figure 3
The thermodynamic diagram about the betweenness centrality of each port.In order to better demonstrate the distribution effect of port betweenness centrality heat, only the top 34 are shown, and the sum of betweenness centralities exceeds 80% of the port heating, as shown in Figure4.Figure 4
The thermodynamic diagram about rank in the top 34 ports in the betweenness centrality.From the above two thermal distribution charts, it can be seen that most of the ports with large betweenness centrality values are distributed in the channels between the major oceans; it can be seen that the distribution of port betweenness centrality heat is consistent with the actual situation of the major international shipping paths, indicating that the basic data such as port samples, direct edge processing, and port distance data are reasonable and effective and that the algorithm is feasible and effective to carry out strategic pivots analysis of the port network.


## 4.3. Superior Analysis and Verification of the Port Strategic Importance

According to the model solution principle of betweenness centrality, the greater the betweenness centrality value of a dot in the network, which indicates closer connection between the dot and other networks in the network, the greater the influence, the greater the role played on the network, and the greater the strategic importance.According to the third part of the clustering algorithm, the training results show that when the three sets of data differenceZmin = 35688.46, the three centers are 4706.16, 1479.56, and 61.73; the strategic importance of the “superior” group has 12 ports, “general” group has 30 ports, and “inferior” group has 113 ports, as in Table 6.Table 6
Group results by interstitial central numerical training (ports in the “inferior” group are not listed; specific and available data can be searched or downloaded from the Table Port Betweenness Centrality in the following link:https://doi.org/10.4121/14298851).
Strategic importanceThe list of ports“Superior” group (12)Fremantle Port, Aden Port, Singapore Port, Panama City Port, New York Port, Cape Town Port, Colon Port, Hong Kong, Nouakchott Port, Santos Port, Piraeus Port Terminal, Cherchell Port“General” group (30)Por Said Port, Jeddah, Suez Port, Santo Domingo Port, the Port of Gibraltar, Walvis Port, Mumbai Port, Gwadar Port, Sao Tome and Principe Port, Colombo Port, Tangier Port, Montreal Port, Wado Port, Jakarta-Kariburu, Istanbul Port, Tunisia Port, Punta Arenas Port, Cabesas Port, Pilon Port, London Port, Yokohama Port, Tanjung Priok, Abu Dhabi Port, the Kingdom of Denmark, Monrovia Port, Shanghai Port, Salalah Port, Durban Port, Port-au-Prince, Havana PortFor the above training results, the grouping results were analyzed by Kruskal–Wallis test, as in Table7.Table 7
Kruskal–Wallis test grouping results.
VariableConstituenciesAverageStandard deviationThe number of samplesKruskal–Wallis inspectionThe card square valueP valueThe number of ports crossed by the shortest pathThe first group (superior)4557.80940.661225.12∗∗∗P ≤ 0.01The second group (general)1617.6554.1230The second group (general)1617.6554.123070.63∗∗∗P ≤ 0.01The third group (inferior)133.48171.87113According to the above test results, the average variance of the three sets of data is less than 0.01%.


## 5. Conclusions

The number of ports is crossed by the shortest path and betweenness centrality of the two simulations of the port in the network as “superior,” “general,” and “inferior” groups; the grouping results test is valid, but the results of the grouping are the same, so it is necessary to further the above two simulation results of joint coverage analysis and finally determine the strategic pivots port.Both sets of simulation results are “general” or “inferior” ports of strategic importance; we think that should not be selected as the strategic pivots of the port network; therefore, the two sets of simulation results, only for at least one set of simulation results, show the strategic importance of “superior” ports, a joint coverage analysis. Among them, for the strategic importance of the “superior” group, the number of ports crossed by the shortest path in the “superior” group is 9 ports, the betweenness centrality dimension “superior” group of 12 ports; the specific results can be seen in Table8.Table 8
A joint coverage matrix of strategically important “superior” ports.
The number of ports crossed by the shortest pathSuperiorGeneralInferiorBetweenness centralitySuperiorPiraeus Port Terminal, Aden Port, Cherchell PortHong Kong, Singapore Port, Nouakchott Port, Cape Town Port, Fremantle Port, New York Port, Colon Port, Panama City PortSantos PortGeneralPor Said Port, Suez Port, Tunisia Port, Jeddah, Mumbai Port, Colombo PortInferiorBased on the data in the table above, only the ports in the upper left triangle matrix are strategically important “superior” ports, so the four sets of ports are analyzed.(1)
The strategic importance of both simulation results is that there are three “superior” ports. Geographically, the three ports are located in the channel from the Indian Ocean, through the Red Sea, the Mediterranean Sea and into the Atlantic Ocean, with the Aden Port and the Cherchell Port as the ports at the mouth of the channel, while the Piraeus Port is at the Centre of the Mediterranean Sea and is the main transit point between the ports of European and North African countries. The three ports are located in the busiest shipping lanes in the world, so it is realistic and reasonable that the three ports should be chosen as strategic pivots ports.(2)
The number of ports crossed by the shortest path simulation is grouped as “superior” and the betweenness centrality simulation is grouped into “general” with six ports. Four of these ports are located in the Channel from the Indian Ocean, through the Red Sea, the Mediterranean Sea and into the Atlantic Ocean, while the Mumbai Port and the Colombo Port are located at the Pacific to Indian Ocean exits and are the main shipping lanes connecting the Pacific and the Indian Oceans; from this point of view, the six ports selected as strategic pivot ports are realistic and reasonable.(3)
The number of ports crossed by the shortest path simulation is grouped into “general,” and the betweenness centrality simulation is grouped into “superior” with eight ports. Among them, the Hong Kong and the Singapore Port are located at the entrance of the Pacific to Indian Ocean path, the ports of Nouakchott and Cape Town are located on the southern path between the Indian Ocean and the Atlantic Ocean, and the Colombo Port and the Panama City Port are the two ports connecting the Pacific Ocean and the Atlantic Ocean, while the ports of New York Port and the Fremantle Port are the main points of entry for the North American continent and the Australian mainland. These ports are located on major international paths, so it is realistic and reasonable that they should be chosen as strategic pivot ports.(4)
The number of ports crossed by the shortest path simulation is grouped as “inferior,” and the port with the betweenness centrality simulation grouped as “superior” is only the Santos Port. The Santos Port is an important port in Brazil; from the simulation process, it can be seen that Santos, in the grouping results of the large error, because the route Santos has strong substitutability, and there are more ports on the east coast of the Atlantic than the west coast of the Atlantic; therefore, the Santos Port is divided into the number of ports crossed by the shortest path dimension “down” group. For this reason, the Santos Port should not be chosen as a strategic pivots port.In summary, 17 of the 18 ports with “superior” strategic importance above, with the exception of the Santos Port, have been identified as strategic pivot points of the global port network.


## 6. Suggestions and Discussions

### 6.1. “The Belt and Road” Strategic Pivots Port Analysis and Instructive Suggestions

“The Belt and Road” initiative is a new engine for promoting international capacity cooperation and a strong guarantee for win-win cooperation among the agreed countries. “Belt and Road,” the economic industry across Asia, Europe, and Africa, covers 60% of the world’s population, including 30% of the global economy; there is a huge potential for development. If the “Belt and Road” Agreement is signed in the hinterland of the port, it will certainly get a great deal of assistance in infrastructure and will play a more important role in the economic and trade exchanges between the countries of the agreement.Chinese enterprises are involved in investment, construction, and operation of ports; whether from the commercial logic or from a technical point of view, the future cooperation will greatly improve control and stability. Although there are sovereign barriers between countries, the commercial rules of the world economy run through the beginning and the end of economic development.In view of the 17 ports where the above strategic pivot points are “superior,” if China wants to develop the strategic layout of its port network in the world, it needs to consider the economic development potential of the port network from China’s perspective, as well as the controllability and stability of future cooperation. Therefore, the two attributes of “One Belt and One Road” and “whether Chinese enterprises participate” of these strategic pivot ports are analyzed by analogy analysis. Based on these two attributes, strategic pivot ports are grouped into four categories, as in Table9.Table 9
A double attribute category table for strategic pivot ports.
Whether Chinese companies participate in attributesYesNo“The Belt and Road” country propertiesYesHong Kong, Colombo Port, Piraeus Port Terminal, Cherchell Port, Suez Port, Por Said Port, Nouakchott Port, Colon PortAden Port, Singapore Port, Tunisia Port, Jeddah, Cape Town Port, Panama City PortNoZeroFremantle Port, New York Port, Mumbai PortAccording to the properties of strategic pivots ports, they are analyzed separately and enlightening suggestions are made:(1)
There are eight strategic pivot ports with the participation of Chinese enterprises and hinterland countries that have signed “the Belt and Road” Agreement. From the geographical location of the international shipping paths, two ports are the main ports of the Indo-Pacific sea path (the Indo-Pacific sea path is a sea path connecting India and the Pacific Ocean), four ports are the main ports connecting the Indian Ocean and the Atlantic Ocean north path, a port connects the Atlantic Ocean and the Pacific Ocean, and one of these ports is an important port from Africa radiation to North America, South America, and Europe; from this point of view, these eight ports are located on the main international shipping paths, and comprehensive coverage of several major maritime paths connects several major sea areas. The hinterland countries in which the port is located have signed “the Belt and Road” Agreement, with low political risks and great potential for economic development, and the role of the port in the future economic development process will become more and more important. The port has Chinese enterprises involved in investment, construction, and operation; in the future cooperation of the port, Chinese enterprises will have a strong voice. Therefore, it will play a vital role to give priority to the development of these eight strategic pivot ports and take these eight ports as the core hubs of “the Belt and Road” port network to radiate and lead the economic development of the countries along “the Belt and Roa.”(2)
The port hinterland countries have signed “the Belt and Road” Agreement but there are six strategic pivot ports in which Chinese enterprises are not involved in investment and construction operations. Geographically, it is the Indo-Pacific sea path, the Indo-Atlantic North Sea path, the Indo-Atlantic South Sea path (the Indo-Atlantic North Sea path is a sea path connecting India and the Atlantic Ocean, via the Red Sea and the Mediterranean Sea, and the Indo- Atlantic South sea path is a sea path connecting India and the Atlantic Ocean, through the Mozambique Strait and through South Africa), the Indian-South Sea path refers to the sea path connecting India and the Atlantic Ocean, through the Red Sea, the Mediterranean Sea, the main port of the Atlantic and Pacific Panama paths. The hinterland countries in which these ports are located have signed “the Belt and Road” Agreement, which has a good basis for political and economic cooperation, and need to vigorously promote cooperation between Chinese enterprises and these ports at the commercial or technical level, which is not only conducive to enhancing the stability of “the Belt and Road” port network but also conducive to promoting the participation of these countries in “the Belt and Road” other industrial energy and other aspects of cooperation.(3)
There are three ports where neither attribute is available. Geographically, these ports are not the main sea paths of the port but are important medium-transformation ports. New York Port is the main transshipment port on the west coast of the Atlantic Ocean, Fremantle Port is an important transshipment port to the Australian mainland in other waters, and Mumbai Port is an important transshipment port on the east coast of the Indian Ocean. Therefore, it is necessary to strengthen cooperation with the commercial level of these ports, reduce the transit costs of maritime transport, and enhance the competitiveness of “the Belt and Road” port network.


### 6.2. Discussion of Other Association Studies

This paper abstracts the global port and path into a nondirected power network and considers the shortest path between ports, the shortest path through the port, the betweenness centrality of the port network and other factors, from whether the strategic importance of the port is superior to judge and choose whether it should be identified as the strategic pivot of the global port network; the strategic layout of the global port network to promote “the Belt and Road” along the port economic development has a strong reference significance. However, the influence factors do not take into account the cost of actual shipping, port throughput capacity, and trade volume between countries and other factors; therefore, in practice, the impact factors for further in-depth study can also be increased.


## 6.1. “The Belt and Road” Strategic Pivots Port Analysis and Instructive Suggestions

“The Belt and Road” initiative is a new engine for promoting international capacity cooperation and a strong guarantee for win-win cooperation among the agreed countries. “Belt and Road,” the economic industry across Asia, Europe, and Africa, covers 60% of the world’s population, including 30% of the global economy; there is a huge potential for development. If the “Belt and Road” Agreement is signed in the hinterland of the port, it will certainly get a great deal of assistance in infrastructure and will play a more important role in the economic and trade exchanges between the countries of the agreement.Chinese enterprises are involved in investment, construction, and operation of ports; whether from the commercial logic or from a technical point of view, the future cooperation will greatly improve control and stability. Although there are sovereign barriers between countries, the commercial rules of the world economy run through the beginning and the end of economic development.In view of the 17 ports where the above strategic pivot points are “superior,” if China wants to develop the strategic layout of its port network in the world, it needs to consider the economic development potential of the port network from China’s perspective, as well as the controllability and stability of future cooperation. Therefore, the two attributes of “One Belt and One Road” and “whether Chinese enterprises participate” of these strategic pivot ports are analyzed by analogy analysis. Based on these two attributes, strategic pivot ports are grouped into four categories, as in Table9.Table 9
A double attribute category table for strategic pivot ports.
Whether Chinese companies participate in attributesYesNo“The Belt and Road” country propertiesYesHong Kong, Colombo Port, Piraeus Port Terminal, Cherchell Port, Suez Port, Por Said Port, Nouakchott Port, Colon PortAden Port, Singapore Port, Tunisia Port, Jeddah, Cape Town Port, Panama City PortNoZeroFremantle Port, New York Port, Mumbai PortAccording to the properties of strategic pivots ports, they are analyzed separately and enlightening suggestions are made:(1)
There are eight strategic pivot ports with the participation of Chinese enterprises and hinterland countries that have signed “the Belt and Road” Agreement. From the geographical location of the international shipping paths, two ports are the main ports of the Indo-Pacific sea path (the Indo-Pacific sea path is a sea path connecting India and the Pacific Ocean), four ports are the main ports connecting the Indian Ocean and the Atlantic Ocean north path, a port connects the Atlantic Ocean and the Pacific Ocean, and one of these ports is an important port from Africa radiation to North America, South America, and Europe; from this point of view, these eight ports are located on the main international shipping paths, and comprehensive coverage of several major maritime paths connects several major sea areas. The hinterland countries in which the port is located have signed “the Belt and Road” Agreement, with low political risks and great potential for economic development, and the role of the port in the future economic development process will become more and more important. The port has Chinese enterprises involved in investment, construction, and operation; in the future cooperation of the port, Chinese enterprises will have a strong voice. Therefore, it will play a vital role to give priority to the development of these eight strategic pivot ports and take these eight ports as the core hubs of “the Belt and Road” port network to radiate and lead the economic development of the countries along “the Belt and Roa.”(2)
The port hinterland countries have signed “the Belt and Road” Agreement but there are six strategic pivot ports in which Chinese enterprises are not involved in investment and construction operations. Geographically, it is the Indo-Pacific sea path, the Indo-Atlantic North Sea path, the Indo-Atlantic South Sea path (the Indo-Atlantic North Sea path is a sea path connecting India and the Atlantic Ocean, via the Red Sea and the Mediterranean Sea, and the Indo- Atlantic South sea path is a sea path connecting India and the Atlantic Ocean, through the Mozambique Strait and through South Africa), the Indian-South Sea path refers to the sea path connecting India and the Atlantic Ocean, through the Red Sea, the Mediterranean Sea, the main port of the Atlantic and Pacific Panama paths. The hinterland countries in which these ports are located have signed “the Belt and Road” Agreement, which has a good basis for political and economic cooperation, and need to vigorously promote cooperation between Chinese enterprises and these ports at the commercial or technical level, which is not only conducive to enhancing the stability of “the Belt and Road” port network but also conducive to promoting the participation of these countries in “the Belt and Road” other industrial energy and other aspects of cooperation.(3)
There are three ports where neither attribute is available. Geographically, these ports are not the main sea paths of the port but are important medium-transformation ports. New York Port is the main transshipment port on the west coast of the Atlantic Ocean, Fremantle Port is an important transshipment port to the Australian mainland in other waters, and Mumbai Port is an important transshipment port on the east coast of the Indian Ocean. Therefore, it is necessary to strengthen cooperation with the commercial level of these ports, reduce the transit costs of maritime transport, and enhance the competitiveness of “the Belt and Road” port network.


## 6.2. Discussion of Other Association Studies

This paper abstracts the global port and path into a nondirected power network and considers the shortest path between ports, the shortest path through the port, the betweenness centrality of the port network and other factors, from whether the strategic importance of the port is superior to judge and choose whether it should be identified as the strategic pivot of the global port network; the strategic layout of the global port network to promote “the Belt and Road” along the port economic development has a strong reference significance. However, the influence factors do not take into account the cost of actual shipping, port throughput capacity, and trade volume between countries and other factors; therefore, in practice, the impact factors for further in-depth study can also be increased.



---

*Source: 9967773-2021-05-19.xml*