# Analyzing Interactions between Japanese Ports and the Maritime Silk Road Based on Complex Networks

Authors: Zhi-Hua Hu; Chan-Juan Liu; Paul Tae-Woo Lee
Journal: Complexity
 (2020)

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## Abstract

This article considers how the Japanese ports interact with the ports of China and along the 21st century Maritime Silk Road (MSR) while they are embedded in the global port network, especially in the context of China’s Belt and Road Initiative. At a port level, it primarily uses connectivity analysis to analyze the port relations and significances in the maritime network. In contrast, at the network level, it applies the methods from network sciences to analyze the significances of these maritime networks and the interactions among the maritime networks of Japan, China, and MSR. This article extracts a large-scale maritime network from ports and vessels’ profiles and data of vessels’ Automatic Identification System (AIS). It then examines the relations among the networks (including Japan, China, MSR, and global ports) after defining the maritime networks, network generation schemes, and port network analysis tools. Based on the analysis results and findings, this study draws some implications for regional ports and shipping development and the global supply network.


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## Body

## 1. Introduction

A maritime system consists of ports and shipping lines [1]. A global maritime network undertakes 80–90% cargo trade in the world, and its traffic is even estimated to increase by 240–1,209% by 2050 [2]. This article considers a maritime country as a network of ports. China initiated the Belt and Road Initiative (BRI) comprising of the 21st century Maritime Silk Road (MSR) and the Silk Road Economic Belt (SREB) in 2013 [3]. They also can be taken as maritime networks consisting of the ports and vessel flows along the BRI or MSR. The ports, countries with ports, and regional port systems are interweaved in the complicated global port and shipping networks. Thus, this study attempts to raise and answer a research question: how do the maritime networks represent the country- and region-level interactions embedded in the global maritime network?China publicly released a document entitled “Vision and Actions on Jointly Building Silk Road Economic Belt and 21st-Century Maritime Silk Road” [3, 4]. The document proposed the principles and framework which form the foundation of the BRI, including two parts, MSR and SREB. This article investigates the relation between Japan and MSR. The 21st century Maritime Silk Road goes from China’s coast to Europe through the South China Sea and the Indian Ocean in one route and from China’s coast through the South China Sea to the South Pacific in the other [5]. Since the inception of the BRI in 2013, it has motivated researchers, businessmen, and policy-makers to address its impact in a multidimensional way. The official document of MSR does not include Japan. However, Japan is an ancient maritime country with numerous maritime ports and advanced maritime transport [6]. It locates near one end of the MSR. Most importantly, Japan is an important trade partner of China.Japan has begun to pay more and more attention to the BRI with increasing anticipations [7]. From 2013 to 2015, the Japanese government and the Diets Committee have discussed the Asian Infrastructure Investment Bank (AIIB) membership issue intensively. Only after 2015, the discussion covered the BRI with a wider range of topics. By looking at responses by the Japanese government, the initial response until 2016 was “nonparticipation”; however, after 2017, the government has shifted attitude to “conditional engagement” through business cooperation in the third countries, especially plus-sum dimension [8].Hu et al. [1, 9] have established a port and shipping data system using the data from the Internet and commercial providers. Their studies preprocessed the data of maritime ports (6945 ports), terminals (more than 14322 terminals), and berths based on various port data categories and verified by web crawlers and long-time manual processing. They obtained the vessel profiles mainly by web crawlers and so they may not be complete when comparing the real set of active vessels in the world. The ports and vessels’ profiles may be changed, and seemingly no official or commercial organization manages such data centrally. Therefore, the acquisition and verification of these data are time-consuming. We generated the shipping connections among maritime ports from the vessels’ Automatic Identification System (AIS) (3,000,000 vessels) data of 2016. There is an AIS data-sharing network in the world to ensure vessel traveling safety [10]. The AIS data may be recorded in units of second or minute for each vessel when the AIS devises have been installed. Therefore, the AIS data volume is massive. By the present technologies used by us, it will take at least two months to process the data of 2016. From the vessel tracks recorded in AIS, we identified the vessels’ calling sequences of ports. The data system does not collect the cargo volumes or containers carried by vessels or handled by maritime ports. Therefore, we used the vessels’ weight capacities as estimates of the flows of vessels. As described above, the vessels’ calling sequences of ports can be utilized and so we can establish a maritime network (maritime ports and vessel flows) as the base of this study.This study formulates Japan by a network of its ports and vessel flows among the ports, while the country is not isolated but is connected to other ports, countries, and the global maritime network, as well as China. Simultaneously, China, different countries, and even the global maritime system are all such maritime networks in the global maritime network. The MSR consists of a group of countries, especially with maritime ports and transport connections, which also contribute to a maritime network.In the era of big data, the bridge of data and qualitative methods emerge in industries [11]. Data storytelling case studies become a vital stream of qualitative researches [12, 13]. In this study, we take the Japanese maritime network in the global maritime network and interact with various other maritime networks as a case that consists of a series of analysis driven by the data system and network analysis methods (see Section 3).In the following, we first review the relevant studies that provide general insights into the research question. Then, we develop maritime network analysis methods with eight definitions and computing procedures by extending general network analysis methods. This article used a data system as described in our previous studies [1, 4], and we present the details related to data and visualization in Section 4. Then, a series of scenarios are analyzed using the data system and proposed network analysis methods. Finally, we discuss the study’s empirical findings and conclusions with implications for theory and future research.


## 2. Background and Literature Review

### 2.1. Network Analysis

The study of networks has a long history in graph theory and sociology. The modern chapter of network science emerged in the background of complexity, complex network, and complex system. The most explosive works in network sciences are helpful to the study of random networks in graph theory [14] and the social network [15]. Various complex networks exist in telecommunication networks, computer networks, biological networks, cognitive and semantic networks, and social networks. The emergence of network science presents the following natures: interdisciplinary, empirical, and data-driven, quantitative and mathematical, and computational nature. Thus, many scholars developed various models and algorithms by using principles and technologies in mathematics and computer sciences for analyzing the network natures and characteristics by considering distinct nodes (elements, actors, nodes, or vertices) and the connections (links or edges). Network science provides various methods to assess the node, edge, and network complexities (e.g., centrality analysis [15] and link prediction [16]), detect the network structures (e.g., clustering and community analysis [17, 18]), and examine the network behaviors (e.g., synchronization and diffusion [19, 20]).In this study, upon network science, the maritime networks and their relations are examined. We formulate the countries and regions as maritime networks and their interactions. Thus, the methods in network science can be used and tuned to analyze the shipping, cargo, and trade relations in the port, country, region, and global levels with different granularities of stakeholders.


### 2.2. Maritime Networks

In a maritime network, a maritime port itself is a hierarchical organization generally with some terminals that contain berths as primary vessel handling facilities; additionally, a port is also a part of a port city that borders with its hinterlands [1]. Due to these hierarchies, the maritime network is geographically a multilayer multiscale system. Meanwhile, it is also associated with logistics, supply chain, industrial chain, trade, and even societies and environments. In this article, we restrict the maritime network to a network of ports and shipping connections; then, we investigate the relations between ports and countries (or independent economies and regions) based on this network.The maritime network studies can be categorized into three by the method used. First, the maritime networks are studied by network programming to optimize the network structures or deploy the resources operating the networks [21, 22]. Second, many studies investigate the characteristics of finely modeled networks by using the complex network and social network analysis methods [23–25]. Third, the maritime networks are studied broadly by using comprehensive methods [3, 4]. This article belongs to the second category. In Table 1, we reviewed ten studies and identified a set of networks and analysis methods: the original data of constructing the networks mainly come from yearbooks, Internet data queries, and AIS data; analysis methods mainly include centrality, attack test, clustering, and community detection.Table 1
Maritime network studies using network analysis methods.
No.ArticlesNetworksAnalysis methods1[26](1) Containerized maritime network (1164–1342 vessels and 330–390 ports); (2) general cargo maritime network (1515–1654 vessels and 938–1232 ports); (3) the data were queried from the Lloyd’s Register database (generated using AIS data).Centrality analysis.2[27](1) Containerized maritime network for the East-West corridor from 1995 to 2011; (2) the network was constructed by the Containerization International Yearbooks (2012).Degree centrality and distribution, concentration, and regional network analysis.3[23]The Greek Maritime Transportation Network (GMN) is a maritime transportation system that connects 229 ports among regions of Greece.Centrality, clustering, modularity, average path length, and degree distribution analysis.4[25]A network (2001–2012) among 17 regions comes from the International Containerization (CI-Online) database that provides container deployment data (in TEU) among world regions of the top 100 container lines in terms of the total TEU capacity, and it updates monthly.Centrality and vulnerability analysis.5[28]The baseline container shipping network (2012) has 1113 nodes and 15916 links obtained from Lloyd’s List Intelligence.Centrality, community, degree distribution, and vulnerability analysis.6[24](1) The maritime container transportation network consisted of 39 major container ports, including the 18 major container ports in East Asia, with a throughput of a minimum of 1.5 million TEUs. in 2013; (2) edges between ports are weighted by the weekly transportation capacity (in TEUs) deployed by the top 20 liner shipping companies; (3) the typical transit time between pairs of ports is estimated based onhttp://www.searates.com.Centrality analysis.7[29](1) A multiplex shipping network used the data on liner shipping services in the Americas for the 32 countries and the 139 container ports located in them; (2) the primary data source is the Containerization International Yearbook (2011).Centrality, clustering, attack simulation, and vulnerability analysis.8[30](1) Created a container shipping network by using the data from Alphaliner in 2014; (2) the network comprises 439 nodes and 2331 edges.Centrality, core-periphery, and community analysis.9[31]Based on the AIS data, from January 2014 to March 2015, three maritime networks were built: the container shipping network has 577 nodes and 5794 edges; the tanker shipping network has 708 nodes and 13,935 edges; the bulk carrier shipping network has 700 nodes and 15,337 edges in the MSR shipping network.Degree distribution, centrality, and flow spatial distribution analysis.10[32](1) Used AIS data to build three cargo ship transportation networks (oil tanker, container ship, and bulk carrier); (2) the container, oil tanker, and bulk carrier ship networks contain 1488, 2042, and 1969 ports individually.Centrality, degree distribution, attack analysis, and network robustness assessment.11[33]The Greek Maritime Network connects 229 ports via 231 bidirectional shipping routes.Graph density, centrality, clustering, modularity, and average path length.Source: compiled by the authors.


### 2.3. Japanese Maritime Network

Japan is a typical maritime country. In our data system, Japan has 994 ports in total, of which 125 ports are considered essential both in international and domestic maritime networks [34]. Maritime ports are critically crucial to the national and local economies. Because Japan is mountainous, major metropolitan areas are all developed on the coastal planes of the country. The three most significant metropolitan areas of Kanto, Chukyo, and Kinki are all developed along with the large terminals, namely, the Bays of Tokyo, Ise, and Osaka, respectively [34]. Historically, large maritime ports have played a critically important role in the economy as well as the urban development of these bay areas.Developing a maritime system is critically important to Japan. First, Japan heavily depends on the import of raw materials for domestic production and the daily life of people. For instance, Japan imported more than 90% of energy and more than 60% of foods from overseas. Japan is a leading hi-tech country, and many industrial products are exported to the world market by seaborne trade. Second, Japan consists of about 6,800 islands, including four main islands. Most cities develop along the coastal lines of the country, and each of them has developed its port. Ports are critical to the local economy and development. Third, the cost of developing Japanese ports is high and increasing due to severe ocean conditions. Port investment is infeasible when the government cannot recognize the ports as essential parts of the development strategies of the nation and local governments. Fourth, limited land availability of port cities restricts the Japanese port developments. The marine terminals, logistics activities, and the port cities demand a large volume of lands. Therefore, the governments must optimize the lands’ efficiency and develop multiuse modes to cope with these conditions. Due to severe trade and economic dependence on maritime transport and shortage of land resources, Japanese ports and the shipping industry faces fierce competition in domestic markets and the Asian maritime system. South Korea and China both present competitive power in ports and shipping. The interaction between Japan and neighborhoods and the embeddedness in the global maritime network may indicate potential opportunities for the Japanese port system.


### 2.4. Summary

The network and maritime studies suggest that network formulation of the maritime network of ports and shipping is beneficial to investigate the structures and behaviors of maritime networks. However, existing studies [26, 32] mainly focused on a single network for a country of a region, the network analysis methods coupling two or more maritime networks is still in development. Considering Japan and its interactions with other countries or regions, it is challenging to construct large-scale networks for analysis.


## 2.1. Network Analysis

The study of networks has a long history in graph theory and sociology. The modern chapter of network science emerged in the background of complexity, complex network, and complex system. The most explosive works in network sciences are helpful to the study of random networks in graph theory [14] and the social network [15]. Various complex networks exist in telecommunication networks, computer networks, biological networks, cognitive and semantic networks, and social networks. The emergence of network science presents the following natures: interdisciplinary, empirical, and data-driven, quantitative and mathematical, and computational nature. Thus, many scholars developed various models and algorithms by using principles and technologies in mathematics and computer sciences for analyzing the network natures and characteristics by considering distinct nodes (elements, actors, nodes, or vertices) and the connections (links or edges). Network science provides various methods to assess the node, edge, and network complexities (e.g., centrality analysis [15] and link prediction [16]), detect the network structures (e.g., clustering and community analysis [17, 18]), and examine the network behaviors (e.g., synchronization and diffusion [19, 20]).In this study, upon network science, the maritime networks and their relations are examined. We formulate the countries and regions as maritime networks and their interactions. Thus, the methods in network science can be used and tuned to analyze the shipping, cargo, and trade relations in the port, country, region, and global levels with different granularities of stakeholders.


## 2.2. Maritime Networks

In a maritime network, a maritime port itself is a hierarchical organization generally with some terminals that contain berths as primary vessel handling facilities; additionally, a port is also a part of a port city that borders with its hinterlands [1]. Due to these hierarchies, the maritime network is geographically a multilayer multiscale system. Meanwhile, it is also associated with logistics, supply chain, industrial chain, trade, and even societies and environments. In this article, we restrict the maritime network to a network of ports and shipping connections; then, we investigate the relations between ports and countries (or independent economies and regions) based on this network.The maritime network studies can be categorized into three by the method used. First, the maritime networks are studied by network programming to optimize the network structures or deploy the resources operating the networks [21, 22]. Second, many studies investigate the characteristics of finely modeled networks by using the complex network and social network analysis methods [23–25]. Third, the maritime networks are studied broadly by using comprehensive methods [3, 4]. This article belongs to the second category. In Table 1, we reviewed ten studies and identified a set of networks and analysis methods: the original data of constructing the networks mainly come from yearbooks, Internet data queries, and AIS data; analysis methods mainly include centrality, attack test, clustering, and community detection.Table 1
Maritime network studies using network analysis methods.
No.ArticlesNetworksAnalysis methods1[26](1) Containerized maritime network (1164–1342 vessels and 330–390 ports); (2) general cargo maritime network (1515–1654 vessels and 938–1232 ports); (3) the data were queried from the Lloyd’s Register database (generated using AIS data).Centrality analysis.2[27](1) Containerized maritime network for the East-West corridor from 1995 to 2011; (2) the network was constructed by the Containerization International Yearbooks (2012).Degree centrality and distribution, concentration, and regional network analysis.3[23]The Greek Maritime Transportation Network (GMN) is a maritime transportation system that connects 229 ports among regions of Greece.Centrality, clustering, modularity, average path length, and degree distribution analysis.4[25]A network (2001–2012) among 17 regions comes from the International Containerization (CI-Online) database that provides container deployment data (in TEU) among world regions of the top 100 container lines in terms of the total TEU capacity, and it updates monthly.Centrality and vulnerability analysis.5[28]The baseline container shipping network (2012) has 1113 nodes and 15916 links obtained from Lloyd’s List Intelligence.Centrality, community, degree distribution, and vulnerability analysis.6[24](1) The maritime container transportation network consisted of 39 major container ports, including the 18 major container ports in East Asia, with a throughput of a minimum of 1.5 million TEUs. in 2013; (2) edges between ports are weighted by the weekly transportation capacity (in TEUs) deployed by the top 20 liner shipping companies; (3) the typical transit time between pairs of ports is estimated based onhttp://www.searates.com.Centrality analysis.7[29](1) A multiplex shipping network used the data on liner shipping services in the Americas for the 32 countries and the 139 container ports located in them; (2) the primary data source is the Containerization International Yearbook (2011).Centrality, clustering, attack simulation, and vulnerability analysis.8[30](1) Created a container shipping network by using the data from Alphaliner in 2014; (2) the network comprises 439 nodes and 2331 edges.Centrality, core-periphery, and community analysis.9[31]Based on the AIS data, from January 2014 to March 2015, three maritime networks were built: the container shipping network has 577 nodes and 5794 edges; the tanker shipping network has 708 nodes and 13,935 edges; the bulk carrier shipping network has 700 nodes and 15,337 edges in the MSR shipping network.Degree distribution, centrality, and flow spatial distribution analysis.10[32](1) Used AIS data to build three cargo ship transportation networks (oil tanker, container ship, and bulk carrier); (2) the container, oil tanker, and bulk carrier ship networks contain 1488, 2042, and 1969 ports individually.Centrality, degree distribution, attack analysis, and network robustness assessment.11[33]The Greek Maritime Network connects 229 ports via 231 bidirectional shipping routes.Graph density, centrality, clustering, modularity, and average path length.Source: compiled by the authors.


## 2.3. Japanese Maritime Network

Japan is a typical maritime country. In our data system, Japan has 994 ports in total, of which 125 ports are considered essential both in international and domestic maritime networks [34]. Maritime ports are critically crucial to the national and local economies. Because Japan is mountainous, major metropolitan areas are all developed on the coastal planes of the country. The three most significant metropolitan areas of Kanto, Chukyo, and Kinki are all developed along with the large terminals, namely, the Bays of Tokyo, Ise, and Osaka, respectively [34]. Historically, large maritime ports have played a critically important role in the economy as well as the urban development of these bay areas.Developing a maritime system is critically important to Japan. First, Japan heavily depends on the import of raw materials for domestic production and the daily life of people. For instance, Japan imported more than 90% of energy and more than 60% of foods from overseas. Japan is a leading hi-tech country, and many industrial products are exported to the world market by seaborne trade. Second, Japan consists of about 6,800 islands, including four main islands. Most cities develop along the coastal lines of the country, and each of them has developed its port. Ports are critical to the local economy and development. Third, the cost of developing Japanese ports is high and increasing due to severe ocean conditions. Port investment is infeasible when the government cannot recognize the ports as essential parts of the development strategies of the nation and local governments. Fourth, limited land availability of port cities restricts the Japanese port developments. The marine terminals, logistics activities, and the port cities demand a large volume of lands. Therefore, the governments must optimize the lands’ efficiency and develop multiuse modes to cope with these conditions. Due to severe trade and economic dependence on maritime transport and shortage of land resources, Japanese ports and the shipping industry faces fierce competition in domestic markets and the Asian maritime system. South Korea and China both present competitive power in ports and shipping. The interaction between Japan and neighborhoods and the embeddedness in the global maritime network may indicate potential opportunities for the Japanese port system.


## 2.4. Summary

The network and maritime studies suggest that network formulation of the maritime network of ports and shipping is beneficial to investigate the structures and behaviors of maritime networks. However, existing studies [26, 32] mainly focused on a single network for a country of a region, the network analysis methods coupling two or more maritime networks is still in development. Considering Japan and its interactions with other countries or regions, it is challenging to construct large-scale networks for analysis.


## 3. Maritime Network Analysis Methods

### 3.1. A Systematic Framework

Figure1 presents a systematic framework for this study. Considering the knowledge of interactions among the global maritime network, Japan, China, and MSR, we develop four modules in this study as a too-level framework. First, the previous study on the Shipping Earth data system [1, 4] is the base of this study. Second, we construct the maritime networks as the base of analysis. Third, in the analysis module, eight scenarios are investigated by constructing assessment methods for maritime network analysis. We demonstrate all these data systems, developed concepts, and methods by using the data system.Figure 1
A systematic framework.The global maritime network is defined, followed by general maritime networks. Then, we elucidate two network generation procedures and schemes: we generate a network from a vessel’s port calling sequence; we construct a new network from these two interconnected maritime networks. Finally, the network analyzing methods mainly used in this study (Section5) are given based on the abovementioned network notations. Based on the degree and PageRank centralities, we conceptualize a metric using the flows among nodes as primary (or top-n) flows and significances of flow interactions among the maritime networks.


### 3.2. Maritime Networks

#### 3.2.1. Structures of Maritime Networks

We denote a global maritime network asG=N,E,P,W, where N,E,P,W are the port set, connection set, port properties, and connection properties. E=i,ji,j∈N; P=Pk, Pk=Pik,i∈N; W=Wk, Wk=Pek,e∈E. Here, k is the name or index of properties, and each property is a vector corresponding to the set of nodes or connections. The notations starte and ende are used to access the two end nodes of a connection e∈E. Define the operators innodei, outnodei as the sets of nodes targeting or originating from the node i, as denoted by the following:(1)innodei=startee∈E,ende=i,i∈N,(2)outnodei=endee∈E,starte=i,i∈N.In (1), the set of nodes entering a node i contains the starting nodes of the edges whose ending nodes are the node i. Similarly, the set of nodes leaving a node i contains the ending nodes of the edges whose starting nodes are the node i.Any maritime network is a part of the global maritime network. Given a node subset,Ns⊆N, a maritime network is denoted as GNs=Ns,ENs,PNs,WNs in the following:.(3)ENs=i,ji∈Ns,j∈Ns⊆E,(4)PNs=PkNs=Piki∈Ns,(5)WNs=WkNs=Peke∈ENs.The maritime network of a given set of portsNs can be reformulated in the form of G=N,E,P,W as defined above. Here, the new port set is Ns. The new edge set contains the edges whose starting and ending nodes that are in Ns, as denoted by (3). The port property set is a set of properties, where a property is a data vector corresponding to Ns, as denoted by (4). Similarly, the edge property set is a set of properties, where a property is a data vector corresponding to the edge set computed by (3).The centrality measures include degree, closeness, and betweenness measures of centrality [15]. These basic centralities assess the importance (in various aspects) of a node in a network.A vessels’ shipping traffic network is different from general connectivity-based networks because a vessel’s movement may depend on several previous calling ports [35]. Based on this observation, we develop the network of calling sequences by considering the vessels’ movements. Besides, because the final network is a composition of all edges generated by the calling sequences, the final network utilized the local information (the calls to neighbor ports) to reduce the random errors in AIS data [36].


#### 3.2.2. Generating Maritime Networks

In the context of maritime studies, we define a calling sequence (denoting a sequence byv in a sequence set V) as a sequence of network nodes and a weight attached to the sequence, namely, N⟶v,Wv, where N⟶v=i1,i2,…,iN⟶v, i∗∈N, and a constant weighted is Ws. The sequence v travels from the port ik to the port ik+j. We say that the sequence travels for j jumps.The network of calling sequence is defined by aN⟶v,Wv. By N⟶v,Wv, a maritime network G=N,E,P,W can be generated as (6)–(8). In (8), W∗v is used to represent the original weight of the calling sequence, while Wv is generated for the network.(6)N=set∪vsetN⟶v,(7)E=i,j∃v,i,j∈N⟶v,(8)Wi,jv=∑i,j∈N⟶vW∗v.In (6)–(8), we generate N,E,W from a set of calling sequences. Notably, a calling sequence visits a series of ports one by one. Therefore, the direct connections from a visited port to an adjacent port just after visiting the port can be extracted from the sequence gradually. That is, a set of N−1 connections (edges) can be extracted from a sequence of N ports, as denoted by (7). For a given sequence, we can calculate and determine some properties, e.g., the weight and size of the vessel of this sequence. Therefore, each edge can inherit the property of the sequence, as denoted by (8).In the abovementioned formulations, only direct transition (one jump) from a port to its adjacent port inN⟶v is used to the network G. Indeed, the transitions from a port to its successors all can present indirect transitions with a multiplier of possible smaller coefficients. In (9), all transitions from a port to its successor in the calling sequence indicate connections among ports; in (10), the weight of a connection is reduced by a multiplier, 1/t2−t1, which indicates that long-distance transition (more jumps) impacts less on the weight. Notably, in (9) and (10), by using i∉N⟶vt1+1∼t2, the jump from node i will “stop” when it meets i.(9)E=i,j∃v∈V,t1<t2,t2−t1>jumps,i∉N⟶vt1+1∼t2:i=N⟶vt1,j=N⟶vt2,(10)Wi,jv=∑i=N⟶vt1,j=N⟶vt2,t1<t2,i∉N⟶vt1+1∼t2,t2−t1>jumpsWi,j∗vt2−t1,∀v∈V.As the difference between (9) and (7), they use one jump or multijumps to construct the sets of edges from a sequence. The number of jumps can amend the impacts on the edge properties, as denoted by (10).Hence, we can set an arbitrary upper boundary number of jumps (jumps≤n) to generate E and Wi,jv, and so the resulting E and Wi,jv are denoted by Ejumps≤n and Wi,jvjumps≤n. The resulting network will also affect the centrality and network analysis results. Therefore, this notation indicates the settings of the upper boundary jump number for generating networks. In this study, we generate the networks used in the following sections with jumps≤15. “Jumps” is a new concept introduced to represent the behaviors of the sequence.N⟶vis a time series and other two accompanied series can be defined, T⟶v and D⟶v, which are the visiting times and durations. By using these two series, N⟶v can be segmented into short series for periodical pattern analysis.We can generate a maritime network from a set of maritime networks whose ports come from the original networks, whose port properties aggregate the properties of the ports, and whose edge connections aggregate the weights of connections between the ports of connections.Given two maritime networks (Na,Nb), new Ec,Pc,Wc are generated as (11)–(16), where ⊗ and ⊕ are aggregate operators upon the properties and weights; ENa,Nb is a set of connections between Na and Nb. Notably, we insert two possible new connections into the connection set Ec when connections exist between the given networks, as denoted by (13) and (14).(11)Nc=Na∪Nb,(12)ENa,Nb=i,ji∈Na,j∈Nb,(13)Ec←a,b,ifENa,Nb>0,(14)Ec←b,a,ifENb,Na>0,(15)P=⊗i∈NaPik,⊗i∈NbPikk,(16)W=⊕e∈ENa,NbWeka,b∈Ec.In (11)–(16), we deduce two maritime networks, Na and Nb. In (11), the nodes of a top network come from these subnetworks. In (12), an operator computes the edge set between the nodes of two networks. In (13) and (14), if there are edges between two networks, an edge is added to the edge set of the top network. The node and edge property sets are different. Hence, we introduce aggregation operators in (15) and (16). For example, the throughput property of a network is the sum (⊗=+) of the throughputs of the port nodes of the network. Similarly, the transportation volume between two networks is the sum (⊕=+) of the volumes of all edges between these two networks.


### 3.3. Analysis Tools for Maritime Networks

Two categories of network analysis are studied here: node-based and edge-based analysis tools.


#### 3.3.1. Node-Based Analysis

The node-based tools are defined based on centralities in complex networks, namely, the degree centrality and PageRank centrality [37]. The degree centrality can represent the significance of nodes with inflows and outflows (delegating the port throughputs in maritime studies). In contrast, the PageRank centrality can reflect the network significance of a node (delegating some important hub ports in a maritime network).We derive the definitions of the weighted degree centrality as (17)–(19) [15], where Cindegreei and Coutdegreei are in- and out-degrees when the network is considered as a directional one, and Cdegreei is the centrality degree when we consider the network as a bidirectional one. When analyzing connection networks, the degree is simplified to account the connection times, as defined by (20)–(22). Nioi is a set of connected nodes, while the number of connected nodes is Nioi.(17)Cindegreei=∑ende=iWek,∀i∈N,(18)Coutdegreei=∑starte=iWek,∀i∈N,(19)Cdegreei=Cindegreei+Coutdegreei,∀i∈N,(20)Nini=jj,i∈E,∀i∈N,(21)Nouti=ji,j∈E,∀i∈N,(22)Nioi=Nini∪Nouti,∀i∈N.In the PageRank centrality, the importance of the nodes pointing toi represents the importance of a node i, denoted by innodei, while the nodes pointed by connections from i is denoted by outnodei. The PageRank centrality is conceptually defined by(23)Cpageranki=c∑j∈innodeiCpagerankjoutnodej,i∈N.The “PageRank” [38, 39] centrality is rooted in a random walk of the network. Given a node in a graph, we decide the next node with the “Follow Probability” from the set of alternatives (successors) of the current node (neighbors for the undirected case). Otherwise, when a node has no alternatives (successors), the next node is selected from all nodes. We use the PageRank algorithm implemented in MATLAB 2016.


#### 3.3.2. Edge-Based Analysis

Two edge-based tools are defined: the primary flows among a maritime network, and the flows among two maritime networks in the context of the global maritime network.The primary flows are top-N flows between two maritime networks. Given two maritime networks with node setsNa and Nb, the connections from Na to Nb are ENa,Nb. The flow is denoted by Weflow for each e∈ENa,Nb. Hence, the connections can be ranked by the flows decreasingly. The set of the top-N connections is ΔnNa,Nb. Here, n is a number indicating n connections in the set.The mutual maritime flows occur between two maritime networks in the context of a global network. The network flows are assessed in three criteria: number calling sequences, number of calls, and weighted flow volume.Given two node setsNa and Nb as two maritime networks, the three assessment criteria for mutual network flows are FseqNa,Nb, FvisitNa,Nb, and FweightNa,Nb ((24)–(26)).(24)FseqNa,Nb=∑v∈VNa∩N⟶v>0∧Nb∩N⟶v>0,(25)FvisitNa,Nb=∑v∈V,i∈N⟶vi∈Na∧i+1∈Nb,(26)FweightNa,Nb=∑e∈ENa,NbWeflow+∑e∈ENb,NaWeflow.We further explain the abovementioned three criteria. In (24), we compute the number of vessels’ calling sequences visiting the two maritime networks (visiting a port in a maritime network and visiting another port in another maritime network), which is approximately equal to the number of vessels calling the two maritime networks. It can answer the general question: how many vessels visit the two maritime networks simultaneously? The number should represent the connection strength of two maritime networks. In (25), if a sequence visits a port in a maritime network and then a port in another maritime network, Fvisit will be increased by one. That is to answer the question: how many visits to the two maritime networks? Similarly, by (26), we try to answer: how much volume on the visits between the two networks when the edge property is volume? By these three computing formulas, the relations between the two networks are determined.


### 3.4. An Example

Considering two calling sequences or maritime ports,1,2,3,4,5,6,5,3 with a flow of 500 tons and 2,3,4,5,7,3,1 with 700 tons. The berths of the ports 1–7 are 4, 4, 3, 3, 5, 5, and 5 individually. Therefore, a network G=N,E,P,W can be established:(1)
N=1,2,…,7(2)
Consider a set of eight edges:E=1,2,2,3,3,4,5,6,5,3,5,7,7,3,3,1(3)
P=Pberths and Pberths=4,4,3,3,5,5,5(4)
W=Wflow and Wflow=500,1200,1200,1200,500,700,700,700We can identify two maritime networks from the seven maritime ports, namely,Na=1,2,3 and Nb=4,5,6,7. Set two aggregate operators ⊗ and ⊕ to ∑. A new network of the submaritime networks Gc=Nc,Ec,Pc,Wc can be extracted:(1)
Nc=a,b(2)
Ec=a,b,b,a(3)
Pc=Pberths, and Pberths=11=4+4+3,18=3+5+5+5(4)
Wc=Wflow, and Wflow=1200,1900=1200+700


## 3.1. A Systematic Framework

Figure1 presents a systematic framework for this study. Considering the knowledge of interactions among the global maritime network, Japan, China, and MSR, we develop four modules in this study as a too-level framework. First, the previous study on the Shipping Earth data system [1, 4] is the base of this study. Second, we construct the maritime networks as the base of analysis. Third, in the analysis module, eight scenarios are investigated by constructing assessment methods for maritime network analysis. We demonstrate all these data systems, developed concepts, and methods by using the data system.Figure 1
A systematic framework.The global maritime network is defined, followed by general maritime networks. Then, we elucidate two network generation procedures and schemes: we generate a network from a vessel’s port calling sequence; we construct a new network from these two interconnected maritime networks. Finally, the network analyzing methods mainly used in this study (Section5) are given based on the abovementioned network notations. Based on the degree and PageRank centralities, we conceptualize a metric using the flows among nodes as primary (or top-n) flows and significances of flow interactions among the maritime networks.


## 3.2. Maritime Networks

### 3.2.1. Structures of Maritime Networks

We denote a global maritime network asG=N,E,P,W, where N,E,P,W are the port set, connection set, port properties, and connection properties. E=i,ji,j∈N; P=Pk, Pk=Pik,i∈N; W=Wk, Wk=Pek,e∈E. Here, k is the name or index of properties, and each property is a vector corresponding to the set of nodes or connections. The notations starte and ende are used to access the two end nodes of a connection e∈E. Define the operators innodei, outnodei as the sets of nodes targeting or originating from the node i, as denoted by the following:(1)innodei=startee∈E,ende=i,i∈N,(2)outnodei=endee∈E,starte=i,i∈N.In (1), the set of nodes entering a node i contains the starting nodes of the edges whose ending nodes are the node i. Similarly, the set of nodes leaving a node i contains the ending nodes of the edges whose starting nodes are the node i.Any maritime network is a part of the global maritime network. Given a node subset,Ns⊆N, a maritime network is denoted as GNs=Ns,ENs,PNs,WNs in the following:.(3)ENs=i,ji∈Ns,j∈Ns⊆E,(4)PNs=PkNs=Piki∈Ns,(5)WNs=WkNs=Peke∈ENs.The maritime network of a given set of portsNs can be reformulated in the form of G=N,E,P,W as defined above. Here, the new port set is Ns. The new edge set contains the edges whose starting and ending nodes that are in Ns, as denoted by (3). The port property set is a set of properties, where a property is a data vector corresponding to Ns, as denoted by (4). Similarly, the edge property set is a set of properties, where a property is a data vector corresponding to the edge set computed by (3).The centrality measures include degree, closeness, and betweenness measures of centrality [15]. These basic centralities assess the importance (in various aspects) of a node in a network.A vessels’ shipping traffic network is different from general connectivity-based networks because a vessel’s movement may depend on several previous calling ports [35]. Based on this observation, we develop the network of calling sequences by considering the vessels’ movements. Besides, because the final network is a composition of all edges generated by the calling sequences, the final network utilized the local information (the calls to neighbor ports) to reduce the random errors in AIS data [36].


### 3.2.2. Generating Maritime Networks

In the context of maritime studies, we define a calling sequence (denoting a sequence byv in a sequence set V) as a sequence of network nodes and a weight attached to the sequence, namely, N⟶v,Wv, where N⟶v=i1,i2,…,iN⟶v, i∗∈N, and a constant weighted is Ws. The sequence v travels from the port ik to the port ik+j. We say that the sequence travels for j jumps.The network of calling sequence is defined by aN⟶v,Wv. By N⟶v,Wv, a maritime network G=N,E,P,W can be generated as (6)–(8). In (8), W∗v is used to represent the original weight of the calling sequence, while Wv is generated for the network.(6)N=set∪vsetN⟶v,(7)E=i,j∃v,i,j∈N⟶v,(8)Wi,jv=∑i,j∈N⟶vW∗v.In (6)–(8), we generate N,E,W from a set of calling sequences. Notably, a calling sequence visits a series of ports one by one. Therefore, the direct connections from a visited port to an adjacent port just after visiting the port can be extracted from the sequence gradually. That is, a set of N−1 connections (edges) can be extracted from a sequence of N ports, as denoted by (7). For a given sequence, we can calculate and determine some properties, e.g., the weight and size of the vessel of this sequence. Therefore, each edge can inherit the property of the sequence, as denoted by (8).In the abovementioned formulations, only direct transition (one jump) from a port to its adjacent port inN⟶v is used to the network G. Indeed, the transitions from a port to its successors all can present indirect transitions with a multiplier of possible smaller coefficients. In (9), all transitions from a port to its successor in the calling sequence indicate connections among ports; in (10), the weight of a connection is reduced by a multiplier, 1/t2−t1, which indicates that long-distance transition (more jumps) impacts less on the weight. Notably, in (9) and (10), by using i∉N⟶vt1+1∼t2, the jump from node i will “stop” when it meets i.(9)E=i,j∃v∈V,t1<t2,t2−t1>jumps,i∉N⟶vt1+1∼t2:i=N⟶vt1,j=N⟶vt2,(10)Wi,jv=∑i=N⟶vt1,j=N⟶vt2,t1<t2,i∉N⟶vt1+1∼t2,t2−t1>jumpsWi,j∗vt2−t1,∀v∈V.As the difference between (9) and (7), they use one jump or multijumps to construct the sets of edges from a sequence. The number of jumps can amend the impacts on the edge properties, as denoted by (10).Hence, we can set an arbitrary upper boundary number of jumps (jumps≤n) to generate E and Wi,jv, and so the resulting E and Wi,jv are denoted by Ejumps≤n and Wi,jvjumps≤n. The resulting network will also affect the centrality and network analysis results. Therefore, this notation indicates the settings of the upper boundary jump number for generating networks. In this study, we generate the networks used in the following sections with jumps≤15. “Jumps” is a new concept introduced to represent the behaviors of the sequence.N⟶vis a time series and other two accompanied series can be defined, T⟶v and D⟶v, which are the visiting times and durations. By using these two series, N⟶v can be segmented into short series for periodical pattern analysis.We can generate a maritime network from a set of maritime networks whose ports come from the original networks, whose port properties aggregate the properties of the ports, and whose edge connections aggregate the weights of connections between the ports of connections.Given two maritime networks (Na,Nb), new Ec,Pc,Wc are generated as (11)–(16), where ⊗ and ⊕ are aggregate operators upon the properties and weights; ENa,Nb is a set of connections between Na and Nb. Notably, we insert two possible new connections into the connection set Ec when connections exist between the given networks, as denoted by (13) and (14).(11)Nc=Na∪Nb,(12)ENa,Nb=i,ji∈Na,j∈Nb,(13)Ec←a,b,ifENa,Nb>0,(14)Ec←b,a,ifENb,Na>0,(15)P=⊗i∈NaPik,⊗i∈NbPikk,(16)W=⊕e∈ENa,NbWeka,b∈Ec.In (11)–(16), we deduce two maritime networks, Na and Nb. In (11), the nodes of a top network come from these subnetworks. In (12), an operator computes the edge set between the nodes of two networks. In (13) and (14), if there are edges between two networks, an edge is added to the edge set of the top network. The node and edge property sets are different. Hence, we introduce aggregation operators in (15) and (16). For example, the throughput property of a network is the sum (⊗=+) of the throughputs of the port nodes of the network. Similarly, the transportation volume between two networks is the sum (⊕=+) of the volumes of all edges between these two networks.


## 3.2.1. Structures of Maritime Networks

We denote a global maritime network asG=N,E,P,W, where N,E,P,W are the port set, connection set, port properties, and connection properties. E=i,ji,j∈N; P=Pk, Pk=Pik,i∈N; W=Wk, Wk=Pek,e∈E. Here, k is the name or index of properties, and each property is a vector corresponding to the set of nodes or connections. The notations starte and ende are used to access the two end nodes of a connection e∈E. Define the operators innodei, outnodei as the sets of nodes targeting or originating from the node i, as denoted by the following:(1)innodei=startee∈E,ende=i,i∈N,(2)outnodei=endee∈E,starte=i,i∈N.In (1), the set of nodes entering a node i contains the starting nodes of the edges whose ending nodes are the node i. Similarly, the set of nodes leaving a node i contains the ending nodes of the edges whose starting nodes are the node i.Any maritime network is a part of the global maritime network. Given a node subset,Ns⊆N, a maritime network is denoted as GNs=Ns,ENs,PNs,WNs in the following:.(3)ENs=i,ji∈Ns,j∈Ns⊆E,(4)PNs=PkNs=Piki∈Ns,(5)WNs=WkNs=Peke∈ENs.The maritime network of a given set of portsNs can be reformulated in the form of G=N,E,P,W as defined above. Here, the new port set is Ns. The new edge set contains the edges whose starting and ending nodes that are in Ns, as denoted by (3). The port property set is a set of properties, where a property is a data vector corresponding to Ns, as denoted by (4). Similarly, the edge property set is a set of properties, where a property is a data vector corresponding to the edge set computed by (3).The centrality measures include degree, closeness, and betweenness measures of centrality [15]. These basic centralities assess the importance (in various aspects) of a node in a network.A vessels’ shipping traffic network is different from general connectivity-based networks because a vessel’s movement may depend on several previous calling ports [35]. Based on this observation, we develop the network of calling sequences by considering the vessels’ movements. Besides, because the final network is a composition of all edges generated by the calling sequences, the final network utilized the local information (the calls to neighbor ports) to reduce the random errors in AIS data [36].


## 3.2.2. Generating Maritime Networks

In the context of maritime studies, we define a calling sequence (denoting a sequence byv in a sequence set V) as a sequence of network nodes and a weight attached to the sequence, namely, N⟶v,Wv, where N⟶v=i1,i2,…,iN⟶v, i∗∈N, and a constant weighted is Ws. The sequence v travels from the port ik to the port ik+j. We say that the sequence travels for j jumps.The network of calling sequence is defined by aN⟶v,Wv. By N⟶v,Wv, a maritime network G=N,E,P,W can be generated as (6)–(8). In (8), W∗v is used to represent the original weight of the calling sequence, while Wv is generated for the network.(6)N=set∪vsetN⟶v,(7)E=i,j∃v,i,j∈N⟶v,(8)Wi,jv=∑i,j∈N⟶vW∗v.In (6)–(8), we generate N,E,W from a set of calling sequences. Notably, a calling sequence visits a series of ports one by one. Therefore, the direct connections from a visited port to an adjacent port just after visiting the port can be extracted from the sequence gradually. That is, a set of N−1 connections (edges) can be extracted from a sequence of N ports, as denoted by (7). For a given sequence, we can calculate and determine some properties, e.g., the weight and size of the vessel of this sequence. Therefore, each edge can inherit the property of the sequence, as denoted by (8).In the abovementioned formulations, only direct transition (one jump) from a port to its adjacent port inN⟶v is used to the network G. Indeed, the transitions from a port to its successors all can present indirect transitions with a multiplier of possible smaller coefficients. In (9), all transitions from a port to its successor in the calling sequence indicate connections among ports; in (10), the weight of a connection is reduced by a multiplier, 1/t2−t1, which indicates that long-distance transition (more jumps) impacts less on the weight. Notably, in (9) and (10), by using i∉N⟶vt1+1∼t2, the jump from node i will “stop” when it meets i.(9)E=i,j∃v∈V,t1<t2,t2−t1>jumps,i∉N⟶vt1+1∼t2:i=N⟶vt1,j=N⟶vt2,(10)Wi,jv=∑i=N⟶vt1,j=N⟶vt2,t1<t2,i∉N⟶vt1+1∼t2,t2−t1>jumpsWi,j∗vt2−t1,∀v∈V.As the difference between (9) and (7), they use one jump or multijumps to construct the sets of edges from a sequence. The number of jumps can amend the impacts on the edge properties, as denoted by (10).Hence, we can set an arbitrary upper boundary number of jumps (jumps≤n) to generate E and Wi,jv, and so the resulting E and Wi,jv are denoted by Ejumps≤n and Wi,jvjumps≤n. The resulting network will also affect the centrality and network analysis results. Therefore, this notation indicates the settings of the upper boundary jump number for generating networks. In this study, we generate the networks used in the following sections with jumps≤15. “Jumps” is a new concept introduced to represent the behaviors of the sequence.N⟶vis a time series and other two accompanied series can be defined, T⟶v and D⟶v, which are the visiting times and durations. By using these two series, N⟶v can be segmented into short series for periodical pattern analysis.We can generate a maritime network from a set of maritime networks whose ports come from the original networks, whose port properties aggregate the properties of the ports, and whose edge connections aggregate the weights of connections between the ports of connections.Given two maritime networks (Na,Nb), new Ec,Pc,Wc are generated as (11)–(16), where ⊗ and ⊕ are aggregate operators upon the properties and weights; ENa,Nb is a set of connections between Na and Nb. Notably, we insert two possible new connections into the connection set Ec when connections exist between the given networks, as denoted by (13) and (14).(11)Nc=Na∪Nb,(12)ENa,Nb=i,ji∈Na,j∈Nb,(13)Ec←a,b,ifENa,Nb>0,(14)Ec←b,a,ifENb,Na>0,(15)P=⊗i∈NaPik,⊗i∈NbPikk,(16)W=⊕e∈ENa,NbWeka,b∈Ec.In (11)–(16), we deduce two maritime networks, Na and Nb. In (11), the nodes of a top network come from these subnetworks. In (12), an operator computes the edge set between the nodes of two networks. In (13) and (14), if there are edges between two networks, an edge is added to the edge set of the top network. The node and edge property sets are different. Hence, we introduce aggregation operators in (15) and (16). For example, the throughput property of a network is the sum (⊗=+) of the throughputs of the port nodes of the network. Similarly, the transportation volume between two networks is the sum (⊕=+) of the volumes of all edges between these two networks.


## 3.3. Analysis Tools for Maritime Networks

Two categories of network analysis are studied here: node-based and edge-based analysis tools.


### 3.3.1. Node-Based Analysis

The node-based tools are defined based on centralities in complex networks, namely, the degree centrality and PageRank centrality [37]. The degree centrality can represent the significance of nodes with inflows and outflows (delegating the port throughputs in maritime studies). In contrast, the PageRank centrality can reflect the network significance of a node (delegating some important hub ports in a maritime network).We derive the definitions of the weighted degree centrality as (17)–(19) [15], where Cindegreei and Coutdegreei are in- and out-degrees when the network is considered as a directional one, and Cdegreei is the centrality degree when we consider the network as a bidirectional one. When analyzing connection networks, the degree is simplified to account the connection times, as defined by (20)–(22). Nioi is a set of connected nodes, while the number of connected nodes is Nioi.(17)Cindegreei=∑ende=iWek,∀i∈N,(18)Coutdegreei=∑starte=iWek,∀i∈N,(19)Cdegreei=Cindegreei+Coutdegreei,∀i∈N,(20)Nini=jj,i∈E,∀i∈N,(21)Nouti=ji,j∈E,∀i∈N,(22)Nioi=Nini∪Nouti,∀i∈N.In the PageRank centrality, the importance of the nodes pointing toi represents the importance of a node i, denoted by innodei, while the nodes pointed by connections from i is denoted by outnodei. The PageRank centrality is conceptually defined by(23)Cpageranki=c∑j∈innodeiCpagerankjoutnodej,i∈N.The “PageRank” [38, 39] centrality is rooted in a random walk of the network. Given a node in a graph, we decide the next node with the “Follow Probability” from the set of alternatives (successors) of the current node (neighbors for the undirected case). Otherwise, when a node has no alternatives (successors), the next node is selected from all nodes. We use the PageRank algorithm implemented in MATLAB 2016.


### 3.3.2. Edge-Based Analysis

Two edge-based tools are defined: the primary flows among a maritime network, and the flows among two maritime networks in the context of the global maritime network.The primary flows are top-N flows between two maritime networks. Given two maritime networks with node setsNa and Nb, the connections from Na to Nb are ENa,Nb. The flow is denoted by Weflow for each e∈ENa,Nb. Hence, the connections can be ranked by the flows decreasingly. The set of the top-N connections is ΔnNa,Nb. Here, n is a number indicating n connections in the set.The mutual maritime flows occur between two maritime networks in the context of a global network. The network flows are assessed in three criteria: number calling sequences, number of calls, and weighted flow volume.Given two node setsNa and Nb as two maritime networks, the three assessment criteria for mutual network flows are FseqNa,Nb, FvisitNa,Nb, and FweightNa,Nb ((24)–(26)).(24)FseqNa,Nb=∑v∈VNa∩N⟶v>0∧Nb∩N⟶v>0,(25)FvisitNa,Nb=∑v∈V,i∈N⟶vi∈Na∧i+1∈Nb,(26)FweightNa,Nb=∑e∈ENa,NbWeflow+∑e∈ENb,NaWeflow.We further explain the abovementioned three criteria. In (24), we compute the number of vessels’ calling sequences visiting the two maritime networks (visiting a port in a maritime network and visiting another port in another maritime network), which is approximately equal to the number of vessels calling the two maritime networks. It can answer the general question: how many vessels visit the two maritime networks simultaneously? The number should represent the connection strength of two maritime networks. In (25), if a sequence visits a port in a maritime network and then a port in another maritime network, Fvisit will be increased by one. That is to answer the question: how many visits to the two maritime networks? Similarly, by (26), we try to answer: how much volume on the visits between the two networks when the edge property is volume? By these three computing formulas, the relations between the two networks are determined.


## 3.3.1. Node-Based Analysis

The node-based tools are defined based on centralities in complex networks, namely, the degree centrality and PageRank centrality [37]. The degree centrality can represent the significance of nodes with inflows and outflows (delegating the port throughputs in maritime studies). In contrast, the PageRank centrality can reflect the network significance of a node (delegating some important hub ports in a maritime network).We derive the definitions of the weighted degree centrality as (17)–(19) [15], where Cindegreei and Coutdegreei are in- and out-degrees when the network is considered as a directional one, and Cdegreei is the centrality degree when we consider the network as a bidirectional one. When analyzing connection networks, the degree is simplified to account the connection times, as defined by (20)–(22). Nioi is a set of connected nodes, while the number of connected nodes is Nioi.(17)Cindegreei=∑ende=iWek,∀i∈N,(18)Coutdegreei=∑starte=iWek,∀i∈N,(19)Cdegreei=Cindegreei+Coutdegreei,∀i∈N,(20)Nini=jj,i∈E,∀i∈N,(21)Nouti=ji,j∈E,∀i∈N,(22)Nioi=Nini∪Nouti,∀i∈N.In the PageRank centrality, the importance of the nodes pointing toi represents the importance of a node i, denoted by innodei, while the nodes pointed by connections from i is denoted by outnodei. The PageRank centrality is conceptually defined by(23)Cpageranki=c∑j∈innodeiCpagerankjoutnodej,i∈N.The “PageRank” [38, 39] centrality is rooted in a random walk of the network. Given a node in a graph, we decide the next node with the “Follow Probability” from the set of alternatives (successors) of the current node (neighbors for the undirected case). Otherwise, when a node has no alternatives (successors), the next node is selected from all nodes. We use the PageRank algorithm implemented in MATLAB 2016.


## 3.3.2. Edge-Based Analysis

Two edge-based tools are defined: the primary flows among a maritime network, and the flows among two maritime networks in the context of the global maritime network.The primary flows are top-N flows between two maritime networks. Given two maritime networks with node setsNa and Nb, the connections from Na to Nb are ENa,Nb. The flow is denoted by Weflow for each e∈ENa,Nb. Hence, the connections can be ranked by the flows decreasingly. The set of the top-N connections is ΔnNa,Nb. Here, n is a number indicating n connections in the set.The mutual maritime flows occur between two maritime networks in the context of a global network. The network flows are assessed in three criteria: number calling sequences, number of calls, and weighted flow volume.Given two node setsNa and Nb as two maritime networks, the three assessment criteria for mutual network flows are FseqNa,Nb, FvisitNa,Nb, and FweightNa,Nb ((24)–(26)).(24)FseqNa,Nb=∑v∈VNa∩N⟶v>0∧Nb∩N⟶v>0,(25)FvisitNa,Nb=∑v∈V,i∈N⟶vi∈Na∧i+1∈Nb,(26)FweightNa,Nb=∑e∈ENa,NbWeflow+∑e∈ENb,NaWeflow.We further explain the abovementioned three criteria. In (24), we compute the number of vessels’ calling sequences visiting the two maritime networks (visiting a port in a maritime network and visiting another port in another maritime network), which is approximately equal to the number of vessels calling the two maritime networks. It can answer the general question: how many vessels visit the two maritime networks simultaneously? The number should represent the connection strength of two maritime networks. In (25), if a sequence visits a port in a maritime network and then a port in another maritime network, Fvisit will be increased by one. That is to answer the question: how many visits to the two maritime networks? Similarly, by (26), we try to answer: how much volume on the visits between the two networks when the edge property is volume? By these three computing formulas, the relations between the two networks are determined.


## 3.4. An Example

Considering two calling sequences or maritime ports,1,2,3,4,5,6,5,3 with a flow of 500 tons and 2,3,4,5,7,3,1 with 700 tons. The berths of the ports 1–7 are 4, 4, 3, 3, 5, 5, and 5 individually. Therefore, a network G=N,E,P,W can be established:(1)
N=1,2,…,7(2)
Consider a set of eight edges:E=1,2,2,3,3,4,5,6,5,3,5,7,7,3,3,1(3)
P=Pberths and Pberths=4,4,3,3,5,5,5(4)
W=Wflow and Wflow=500,1200,1200,1200,500,700,700,700We can identify two maritime networks from the seven maritime ports, namely,Na=1,2,3 and Nb=4,5,6,7. Set two aggregate operators ⊗ and ⊕ to ∑. A new network of the submaritime networks Gc=Nc,Ec,Pc,Wc can be extracted:(1)
Nc=a,b(2)
Ec=a,b,b,a(3)
Pc=Pberths, and Pberths=11=4+4+3,18=3+5+5+5(4)
Wc=Wflow, and Wflow=1200,1900=1200+700


## 4. Data

In this study, we use the data of more than 300,000 vessels’ AIS tracks and 6000 maritime ports of 2016 to construct a maritime networkG=N,E,P,W by using the methods developed in Section 3. A vessel’s track of its positions recorded in AIS can be processed to be a calling sequence of maritime ports. By this process, we can obtain the port calling sequences of all vessels. Within these vessels, only about two of the third can have port calling sequences. Here, N is a set of maritime ports in the global maritime network; E is a set of connections among ports. We can generate E by the method described in Section 3. P denotes a property, namely, economic entity (ee), P=Pee. The original weight (W∗s in (8) and (10)) of a vessel calling sequence is the weight of the vessel.Useee∈world,Japan,China,MSR to represent the complete port set (world), the Japanese port set (Japan) and Chinese port set (China), and a set of ports along the Maritime Silk Road (MSR), Nworld=N, NJapan, NChina, and NMSR. Their supplementary sets are denoted by ∅ (empty set), N¯Japan, N¯China, and N¯MSR. Additionally, the Japanese ports include two sets, domestic port set NJd and international port set NJi. A Japanese maritime port is called if and only if at least a vessel visits at least one port, not in NJapan. We introduce Visitsn representing the number of vessels visiting Japanese ports for at least n times, as denoted in (27). Besides, in (28), Countriesv computes the number of countries whose ports are visited by the vessel v.(27)Visitsn=∑v∈SFseqNJapan,N¯Japan>n,(28)Countriesv=Pcountryii∈N⟶v,∀v∈V.Table2 summarizes the vessels visiting the Japanese ports NJapan. First, we classify the trading vessels into domestic and international trading vessels. More vessels are international trading vessels visiting the Japanese ports. Only a very few vessels visited Japan once in 2016, while most vessels visited the country for more than ten times. Considering the time of vessel callings, the distributions of vessels to the visiting times (Visitsi−Visitsi+1) and countries (Countriesv) are depicted (see Figure 2).Table 2
Summary of vessel visits to Japanese ports.
Total vesselsNJapan13925Trading vesselsNJdomestic6419NJinternational7506Vessel visitsVisits2003562Visits1005118Visits506772Visits208769Visits1010270Visits113287Visits0−Visits1638Figure 2
Vessel visiting times and countries. (a)Visitsi−Visitsi+1. (b) Countriesv.
(a)(b)Further, the distributions ofFvisit and Fweight computed from N⟶v can be depicted for dates and months using T⟶v and D⟶v (see Figure 3). The seasonality of the distribution is slight at least for the distributions of Fvisit and Fweight.Figure 3
Periodical vessel visits and flows. (a)Fvisit by date. (b) Fweight by date. (c) Fvisit by month. (d) Fweight by month.
(a)(b)(c)(d)The jumps have impacts onFweight, Fseq, Nio, and Fvisit (see Figure 4). Therefore, the choice of the parameter “jumps” is essential. When the number is too small, the impacts of indirect connections among ports on the results are not observable. The “jumps” represent the visiting behavior of vessels to the ports. If a vessel visits port A just before port C, the number of jumps is one from C to A; if a vessel visits port A before visiting B and C, the number of jumps is two from C to A (Section 3). In this study, we set the number of jumps to 15 in (9) and (10).Figure 4
Japanese port distributions impacted by jumps. (a)Fweightjumps≤n. (b) Fseqjumps≤n. (c) Niojumps≤n. (d) Fvisitjumps≤n.
(a)(b)(c)(d)


## 5. Results and Analysis

In the following, we construct the maritime networks and analyze the interactions among the maritime networks (NJapan, NChina, NMSR,N¯Japan, N¯China, N¯MSR,NJd,andNJi) in the context of the global network (Nworld) by using the node- and edge-based analysis tools.


### 5.1. One-Jump Connections with the World

As defined in (12), The direct connections (jumps=1,ENJapan,N¯Japan) between Japanese ports (NJapan) and the world (N¯Japan) mean the ones directly connecting the Japanese ports and the ports of all countries/regions (see Figure 5). Here, 26097 connections and 922 ports are involved. In other words, the number of jumps (as defined in Figure 3) is one. The vessel connections (see Figures 5(a) and 5(b)) and the top primary flows (see Figures 5(c) and 5(d) for Δ2000NJapan,N¯Japan) help to identify most maritime trading regions.Figure 5
One-jump connections from Japanese ports to the world. (a) Global view (all). (b) Regional view (all). (c) Global view (top 2000). (d) Regional view (top 2000).
(a)(b)(c)(d)


### 5.2. Multijump Connections with the World

All connections between Japanese ports (NJapan) and the world (N¯Japan) are the ones connecting the Japanese ports and the ports of all countries/regions by various numbers of jumps (jumps>1) (see Figures 6 and 7). Here, 114673 connections and 2520 ports are involved. The maritime trading regions can be identified (see Figures 6(a) and 6(b)), as well as the top primary flows (see Figures 6(c) and 6(d) for Δ2000NJapan,N¯Japan). The settings’ multijump connections reveal possible indirect maritime trading partners for Japan.Figure 6
Multijump connections from Japanese ports. (a) Global view (all). (b) Regional view (all). (c) Global view (Top 2000). (d) Regional view (Top 2000).
(a)(b)(c)(d)Figure 7
The network of the domestic connections among Japanese ports.


### 5.3. The Maritime Network of Domestic Trading Flows

The domestic connections (seeEJd computed by (29)) can be summarized in terms of port connections, vessel visits (NJapan), and flow, as well as the connecting domestic ports (see Table 3). The 149 active ports almost entirely interconnect with each other (see NJd computed by (30)) in the connection graph (see Figure 8). The flow throughput of port i is computed by (31)–(34).(29)EJd=i,ji,j∈E;i,j∈NJapan,(30)NJd=ji,j∈E;i,j∈NJapan∪jj,i∈E;j,i∈N¯Japan,(31)Vesselsi=∑v∈V∃j:N⟶vj=i,(32)Cwindegreedi=∑e∈EJd,ende=iWeflow,∀i∈NJapan,(33)Cwoutdegreedi=∑e∈EJd,starte=iWeflow,∀i∈NJapan,(34)Cwdi=Cwoutdegreedi+Cwoutdegreedi.Table 3
Domestic trading connections among Japanese ports.
NoPortiNJdEJdVesselsiCwdi1Kobe1483080364107938896597652Chiba1483170974177433668942173Higashi-Harima1483141166138733266707834Yokohama1482808952625132384213595Kawasaki1482973261506131025372036Tokyo1482463837867627191770177Osaka1482793249996626806580488Yura1482631439791526120794629Nagoya14826425392824248093423510Shingu14826196463112206113339711Atsumi14825148373972204780686612Omaezaki14826578425549200906706213Kurihama14826087360035170434813314Kashima14825772362319164169660515Wakayama14825682348348162422794816Kinuura14823559292885160132069317Sakai14825455369813158020744618Shimotsu14825646314510155378051219Kisarazu14822072252279145259925620Yokkaichi148241742508121323937715Mean14514416117407588070354Std77372148324785733186Median1471414056969263031014Min95108714889762340Max148317097417743889659765From the top 20 primary flows (Table4), we can identify the primary port connections, by using Δ20NJapan,NJapan. The last three columns are defined by similar formulas, as presented in (24)–(26).Table 4
Primary connections among the Japanese ports.
NoPort 1 (i)Port 2 (j)Fseqi,jFvisiti,jFweighti,j1KobeHigashi-Harima250349492201242452YokohamaKawasaki285429312032499213KobeOsaka262310402018071714KobeYura350172531880524775ChibaKawasaki301378171836819956TokyoYokohama236190431782902547KobeTokyo230135401763063978KobeYokohama268183861694353309ChibaYokohama2603111514718648210KobeKawasaki2551886313928511811NagoyaTokyo2321103313748943412ChibaKobe3072115012518237713NagoyaYokohama2681371812493980514Higashi-HYura3511624712464203315KobeNagoya2651296912185056916TokyoYura2321025112003248817OsakaHigashi-H2372461311895273518OsakaYura2401318411641404419YokohamaYura2831234111537909220ChibaHigashi-Harima24721324114699162The abovementioned analysis provides tools to identify important or potentially critical domestic ports and maritime transport channels for Japan.


### 5.4. The Maritime Network of International Trading Flows

From the resulting international trading connections of 149 Japanese ports (Table5), most Japanese ports (NJapan) connect to more than 1000 ports (in N¯Japan), as defined in (36) where EJi is given by (35), and only one port is purely a domestic trading port. From the top 20 ports with the most significant flows (Table 6), only one port (Yanai, that is the purely domestic port) is listed. Therefore, Japan is a typical maritime country because its ports are almost international active ports.(35)EJi=i,ji,j∈E;i∈NJapan,j∈N¯Japan,(36)NJi=ji,j∈EJi;i∈NJapan,j∈N¯Japan∪jj,i∈E;j∈NJapan,i∈N¯Japan.Table 5
International trading connections of Japanese ports.
NoPort (i)NJiFseqi,NJiFvisiti,NJiFweighti,NJi1Yokohama17003277513577639188941542Kobe18773601914855938586583543Yura1709285929733629361319224Kawasaki16543011511985026644813935Tokyo1272208688183224844609316Chiba1525222237982323810607327Nagoya1362242728259920446769108Higashi-Harima1548239668468419085934869Osaka12271957872866174344135910Atsumi13422250964844162776483111Yokkaichi12841545836013126542601412Kurihama14022006455552125151817413Kashima14131489238522124472804814Shimotsu13741763846588113751401115Hakodate13631192625809112336195116Kinuura12701771544918111738058217Shirashima15172162269880109939618618Kisarazu1263129052799593657423119Omaezaki1088162994339576532436220Yokohama1700327751357763918894154149Yanai13313692Mean625585614577336818333Std427721426068688285152Median5422994375570536055Min13313692Max1877360191485593918894154Table 6
Top 20 connections between Japan and the world.
NoJapanese portiMaritime networkTop 20 portjFseqi,jFvisiti,jFweighti,j1KobeSingaporeSingapore13457671994984202YokohamaSingaporeSingapore12952891823217873YuraSingaporeSingapore13343781654080504YokohamaHong KongHong Kong16752631541322555TokyoHong KongHong Kong16450381480663986ChibaSingaporeSingapore8430911448502617KawasakiSingaporeSingapore9150721436963928KobeHong KongHong Kong15751071406518909TokyoSingaporeSingapore133282511590435410KobeMalaysiaPengerang Terminal121279511276146811NagoyaSingaporeSingapore123364210987548512ChibaMalaysiaPengerang Terminal78164210377627313YuraMalaysiaPengerang Terminal108216410066239314Higashi-HarimaSingaporeSingapore8324989578199215YokohamaChinaChiwan15228509342519916KawasakiMalaysiaPengerang Terminal7825269290115917YuraHong KongHong Kong13831739102816118AtsumiSingaporeSingapore12826859033387119YokohamaMalaysiaPengerang Terminal11824598739569120YokohamaChinaShanghai162470284396110


### 5.5. Primary Maritime Flows between Japan and the World

From the primary flows (Figure8, Δ20NJapan,N¯Japan) between Japan (NJapan) and the world (N¯Japan), all prominent flows are to or from China (NChina), Chinese Hong Kong, and Singapore. From the top 20 connections between Japan and the world (Table 6, Δ20NJapan,N¯Japan), the most prominent flows are active between Japan and the MSR (mainly Hong Kong, Singapore, and Malaysia in NMSR). Hongkong and Singapore are essential hubs for Japanese products’ trade; China is an essential market of Japanese industries.Figure 8
Primary flows between the Japanese ports and the world.The network flows between Japan (NJapan) and the world (N¯Japan) can be computed (see Table 7). By assessing the ratios of the flows between Japanese and the world as presented in the last two rows in Table 8, the flows of Japanese ports contribute less to the global maritime network (0.56∼2.31%), while contributing to its domestic trade dominantly (11.04∼28.89%).Table 7
Ranking Japanese ports by trading-related values.
NoJapanese portiRanked byNioiFseqi,NworldFvisiti,NworldFweighti,Nworld1KobeKobeKobeChibaKobe2YuraYuraYokohamaKobeYokohama3YokohamaYokohamaKawasakiHigashi-HarimaKawasaki4KawasakiKawasakiHigashi-HarimaKawasakiChiba5ShirashimaHigashi-HarimaYuraYokohamaYura6Higashi-HarimaChibaChibaOsakaHigashi-Harima7NagoyaShirashimaNagoyaShinguTokyo8ChibaKashimaAtsumiYuraNagoya9KisarazuKurihamaOsakaNagoyaOsaka10KurihamaWakayamaKurihamaOmaezakiAtsumi11WakayamaShimotsuTokyoTokyoKurihama12KinuuraHakodateShimotsuAtsumiKashima13AtsumiNagoyaOmaezakiKurihamaOmaezaki14SaganosekiAtsumiKinuuraKashimaKinuura15TokyoYokkaichiKashimaSakaiShimotsu16Amagasaki-NATokyoWakayamaWakayamaYokkaichi17KashimaKinuuraShinguShimotsuShingu18OmaezakiKisarazuYokkaichiKomatsushimaKisarazu19ShimotsuSaganosekiShirashimaKinuuraWakayama20YokkaichiOsakaSakaiTakamatsuShirashimaTable 8
Ratios of flows between Japan and the world.
Maritime networkFseqFvisitFweightFlowFJ=F∗NJapan,Nworld3020537196656141.37808E + 11FX=F∗NJapan,N¯Japan872595217200050185931561FW=F∗Nworld,Nworld377863213908291443.89796E + 12Ratio (%)FX/FJ28.8911.0436.42FX/FW2.310.561.29


### 5.6. Ranking Ports by Trading, Connection, and Centralities

Using the global connection data of the Japanese ports, we rank the ports, as shown in Table7. Kobe is the first grade.The Japanese ports are not different in terms of ranking of their throughput (usingCdegreei in Section 3) and network impact (using Cpageranki in Section 3) (see Table 9).Table 9
Ranking the Japanese ports by degree and PageRank centralities.
ThroughputCdegreeiNetwork impactCpagerankiRankPortiRankPorti1Chiba1Chiba2Higashi-Harima2Higashi-Harima3Kobe3Kobe4Kawasaki4Kawasaki5Yokohama5Yokohama6Osaka6Osaka7Shingu7Shingu8Omaezaki8Omaezaki9Yura9Yura10Nagoya10Nagoya11Tokyo11Tokyo12Atsumi12Sakai13Sakai13Atsumi14Kashima14Kashima15Kurihama15Kurihama16Wakayama16Wakayama17Komatsushima17Komatsushima18Shimotsu18Shimotsu19Kinuura19Kinuura20Takamatsu20Takamatsu


### 5.7. Primary Maritime Flows with the Maritime Silk Road

As seen from the primary maritime flows between Japan (NJapan) and the MSR (NMSR) (Figure 9), China, Singapore, and Malaysia are the central import countries connected to Japan.Figure 9
Primary flows between the Japanese ports and the MSR.From the top 20 connections between Japan and MSR (Δ20NJapan,NMSR, Table 10), we can identify three essential stakeholders: Hong Kong, Singapore, and Malaysia along the MSR.Table 10
Top 20 connections between Japan and the MSR.
NoJapan port (i)RegionMSR port (j)Fseqi,jFvisiti,jFweighti,j1KobeSingaporeSingapore13457671994984202YokohamaSingaporeSingapore12952891823217873YuraSingaporeSingapore13343781654080504YokohamaHong KongHong Kong16752631541322555TokyoHong KongHong Kong16450381480663986ChibaSingaporeSingapore8430911448502617KawasakiSingaporeSingapore9150721436963928KobeHong KongHong Kong15751071406518909TokyoSingaporeSingapore133282511590435410KobeMalaysiaPengerang Terminal121279511276146811NagoyaSingaporeSingapore123364210987548512ChibaMalaysiaPengerang Terminal78164210377627313YuraMalaysiaPengerang Terminal108216410066239314Higashi-HarimaSingaporeSingapore8324989578199215YokohamaChinaChiwan15228509342519916KawasakiMalaysiaPengerang Terminal7825269290115917YuraHong KongHong Kong13831739102816118AtsumiSingaporeSingapore12826859033387119YokohamaMalaysiaPengerang Terminal11824598739569120ShanghaiJapanYokohama162470284396110Table11 indicates the ratios of flows between Japan (NJapan) and the MSR (NMSR); about 20% of vessel flows of Japanese international trade are directed to the MSR, while Japan contributes to the MSR by a tiny ratio (from 0.52% to 4.49%) of flows. It implies that although the BRI document has not mentioned Japan, Japan has high connectivity with the BRI at least by the MSR.Table 11
Ratios of flows between Japan and the Maritime Silk Road.
Maritime networkFseqFvisitFweightFlowFJ=F∗NJapan,Nworld3020537196656141.37808E + 11FX=F∗NJapan,NMSR566579156525031290144747FMSR=F∗NMSR,Nworld126273333017036892.64665E + 12Ratio (%)FX/FJ18.767.9622.71FX/FMSR4.490.521.18


### 5.8. Primary Maritime Flows with China

In the connections between Japan (NJapan) and China (NChina) (see Figure 10 and Table 12), Hong Kong, Shanghai, Ningbo, and Guangzhou play essential roles. Although the flows between Japan and China account for 4.59∼9.21% of Japan, while just 0.61∼3.44% of China (see Table 13).Figure 10
Primary flows between Japan and China.Table 12
Top 20 connections between Japan and China.
NoChinese port (i)Japanese port (j)Fseqi,jFvisiti,jFweighti,j1Hong KongYokohama16752631541322552Hong KongTokyo16450381480663983Hong KongKobe15751071406518904ChiwanYokohama1522850934251995Hong KongYura1383173910281616ShanghaiYokohama1624702843961107Hong KongNagoya1353242839807158YangshanYokohama621000757359769Hong KongOsaka14734597261730810ShanghaiKobe18254587178672311ShanghaiTokyo16838097110255012ChiwanTokyo15526946638258513NingboYokohama9516166564457214ChiwanKobe14026086402011215QingdaoYokohama12821246351899716GuangzhouYokohama17518435563671817Hong KongAtsumi14922805543741618ShanghaiOsaka18738045331536619YantianYokohama938375078354020ShanghaiKawasaki152344750111425269 Chinese ports149 Japanese portsTable 13
Ratios of flows between China and Japan.
Maritime networkFseqFvisitFweightFlowFJ=F∗NJapan,Nworld3020537196656141.37808E + 11FX=F∗NJapan,NChina27831190265312468012503FChina=F∗NChina,Nworld80839202849735372.05516E + 12Ratio (%)FX/FJ9.214.599.05FX/FChina3.440.320.61


## 5.1. One-Jump Connections with the World

As defined in (12), The direct connections (jumps=1,ENJapan,N¯Japan) between Japanese ports (NJapan) and the world (N¯Japan) mean the ones directly connecting the Japanese ports and the ports of all countries/regions (see Figure 5). Here, 26097 connections and 922 ports are involved. In other words, the number of jumps (as defined in Figure 3) is one. The vessel connections (see Figures 5(a) and 5(b)) and the top primary flows (see Figures 5(c) and 5(d) for Δ2000NJapan,N¯Japan) help to identify most maritime trading regions.Figure 5
One-jump connections from Japanese ports to the world. (a) Global view (all). (b) Regional view (all). (c) Global view (top 2000). (d) Regional view (top 2000).
(a)(b)(c)(d)


## 5.2. Multijump Connections with the World

All connections between Japanese ports (NJapan) and the world (N¯Japan) are the ones connecting the Japanese ports and the ports of all countries/regions by various numbers of jumps (jumps>1) (see Figures 6 and 7). Here, 114673 connections and 2520 ports are involved. The maritime trading regions can be identified (see Figures 6(a) and 6(b)), as well as the top primary flows (see Figures 6(c) and 6(d) for Δ2000NJapan,N¯Japan). The settings’ multijump connections reveal possible indirect maritime trading partners for Japan.Figure 6
Multijump connections from Japanese ports. (a) Global view (all). (b) Regional view (all). (c) Global view (Top 2000). (d) Regional view (Top 2000).
(a)(b)(c)(d)Figure 7
The network of the domestic connections among Japanese ports.


## 5.3. The Maritime Network of Domestic Trading Flows

The domestic connections (seeEJd computed by (29)) can be summarized in terms of port connections, vessel visits (NJapan), and flow, as well as the connecting domestic ports (see Table 3). The 149 active ports almost entirely interconnect with each other (see NJd computed by (30)) in the connection graph (see Figure 8). The flow throughput of port i is computed by (31)–(34).(29)EJd=i,ji,j∈E;i,j∈NJapan,(30)NJd=ji,j∈E;i,j∈NJapan∪jj,i∈E;j,i∈N¯Japan,(31)Vesselsi=∑v∈V∃j:N⟶vj=i,(32)Cwindegreedi=∑e∈EJd,ende=iWeflow,∀i∈NJapan,(33)Cwoutdegreedi=∑e∈EJd,starte=iWeflow,∀i∈NJapan,(34)Cwdi=Cwoutdegreedi+Cwoutdegreedi.Table 3
Domestic trading connections among Japanese ports.
NoPortiNJdEJdVesselsiCwdi1Kobe1483080364107938896597652Chiba1483170974177433668942173Higashi-Harima1483141166138733266707834Yokohama1482808952625132384213595Kawasaki1482973261506131025372036Tokyo1482463837867627191770177Osaka1482793249996626806580488Yura1482631439791526120794629Nagoya14826425392824248093423510Shingu14826196463112206113339711Atsumi14825148373972204780686612Omaezaki14826578425549200906706213Kurihama14826087360035170434813314Kashima14825772362319164169660515Wakayama14825682348348162422794816Kinuura14823559292885160132069317Sakai14825455369813158020744618Shimotsu14825646314510155378051219Kisarazu14822072252279145259925620Yokkaichi148241742508121323937715Mean14514416117407588070354Std77372148324785733186Median1471414056969263031014Min95108714889762340Max148317097417743889659765From the top 20 primary flows (Table4), we can identify the primary port connections, by using Δ20NJapan,NJapan. The last three columns are defined by similar formulas, as presented in (24)–(26).Table 4
Primary connections among the Japanese ports.
NoPort 1 (i)Port 2 (j)Fseqi,jFvisiti,jFweighti,j1KobeHigashi-Harima250349492201242452YokohamaKawasaki285429312032499213KobeOsaka262310402018071714KobeYura350172531880524775ChibaKawasaki301378171836819956TokyoYokohama236190431782902547KobeTokyo230135401763063978KobeYokohama268183861694353309ChibaYokohama2603111514718648210KobeKawasaki2551886313928511811NagoyaTokyo2321103313748943412ChibaKobe3072115012518237713NagoyaYokohama2681371812493980514Higashi-HYura3511624712464203315KobeNagoya2651296912185056916TokyoYura2321025112003248817OsakaHigashi-H2372461311895273518OsakaYura2401318411641404419YokohamaYura2831234111537909220ChibaHigashi-Harima24721324114699162The abovementioned analysis provides tools to identify important or potentially critical domestic ports and maritime transport channels for Japan.


## 5.4. The Maritime Network of International Trading Flows

From the resulting international trading connections of 149 Japanese ports (Table5), most Japanese ports (NJapan) connect to more than 1000 ports (in N¯Japan), as defined in (36) where EJi is given by (35), and only one port is purely a domestic trading port. From the top 20 ports with the most significant flows (Table 6), only one port (Yanai, that is the purely domestic port) is listed. Therefore, Japan is a typical maritime country because its ports are almost international active ports.(35)EJi=i,ji,j∈E;i∈NJapan,j∈N¯Japan,(36)NJi=ji,j∈EJi;i∈NJapan,j∈N¯Japan∪jj,i∈E;j∈NJapan,i∈N¯Japan.Table 5
International trading connections of Japanese ports.
NoPort (i)NJiFseqi,NJiFvisiti,NJiFweighti,NJi1Yokohama17003277513577639188941542Kobe18773601914855938586583543Yura1709285929733629361319224Kawasaki16543011511985026644813935Tokyo1272208688183224844609316Chiba1525222237982323810607327Nagoya1362242728259920446769108Higashi-Harima1548239668468419085934869Osaka12271957872866174344135910Atsumi13422250964844162776483111Yokkaichi12841545836013126542601412Kurihama14022006455552125151817413Kashima14131489238522124472804814Shimotsu13741763846588113751401115Hakodate13631192625809112336195116Kinuura12701771544918111738058217Shirashima15172162269880109939618618Kisarazu1263129052799593657423119Omaezaki1088162994339576532436220Yokohama1700327751357763918894154149Yanai13313692Mean625585614577336818333Std427721426068688285152Median5422994375570536055Min13313692Max1877360191485593918894154Table 6
Top 20 connections between Japan and the world.
NoJapanese portiMaritime networkTop 20 portjFseqi,jFvisiti,jFweighti,j1KobeSingaporeSingapore13457671994984202YokohamaSingaporeSingapore12952891823217873YuraSingaporeSingapore13343781654080504YokohamaHong KongHong Kong16752631541322555TokyoHong KongHong Kong16450381480663986ChibaSingaporeSingapore8430911448502617KawasakiSingaporeSingapore9150721436963928KobeHong KongHong Kong15751071406518909TokyoSingaporeSingapore133282511590435410KobeMalaysiaPengerang Terminal121279511276146811NagoyaSingaporeSingapore123364210987548512ChibaMalaysiaPengerang Terminal78164210377627313YuraMalaysiaPengerang Terminal108216410066239314Higashi-HarimaSingaporeSingapore8324989578199215YokohamaChinaChiwan15228509342519916KawasakiMalaysiaPengerang Terminal7825269290115917YuraHong KongHong Kong13831739102816118AtsumiSingaporeSingapore12826859033387119YokohamaMalaysiaPengerang Terminal11824598739569120YokohamaChinaShanghai162470284396110


## 5.5. Primary Maritime Flows between Japan and the World

From the primary flows (Figure8, Δ20NJapan,N¯Japan) between Japan (NJapan) and the world (N¯Japan), all prominent flows are to or from China (NChina), Chinese Hong Kong, and Singapore. From the top 20 connections between Japan and the world (Table 6, Δ20NJapan,N¯Japan), the most prominent flows are active between Japan and the MSR (mainly Hong Kong, Singapore, and Malaysia in NMSR). Hongkong and Singapore are essential hubs for Japanese products’ trade; China is an essential market of Japanese industries.Figure 8
Primary flows between the Japanese ports and the world.The network flows between Japan (NJapan) and the world (N¯Japan) can be computed (see Table 7). By assessing the ratios of the flows between Japanese and the world as presented in the last two rows in Table 8, the flows of Japanese ports contribute less to the global maritime network (0.56∼2.31%), while contributing to its domestic trade dominantly (11.04∼28.89%).Table 7
Ranking Japanese ports by trading-related values.
NoJapanese portiRanked byNioiFseqi,NworldFvisiti,NworldFweighti,Nworld1KobeKobeKobeChibaKobe2YuraYuraYokohamaKobeYokohama3YokohamaYokohamaKawasakiHigashi-HarimaKawasaki4KawasakiKawasakiHigashi-HarimaKawasakiChiba5ShirashimaHigashi-HarimaYuraYokohamaYura6Higashi-HarimaChibaChibaOsakaHigashi-Harima7NagoyaShirashimaNagoyaShinguTokyo8ChibaKashimaAtsumiYuraNagoya9KisarazuKurihamaOsakaNagoyaOsaka10KurihamaWakayamaKurihamaOmaezakiAtsumi11WakayamaShimotsuTokyoTokyoKurihama12KinuuraHakodateShimotsuAtsumiKashima13AtsumiNagoyaOmaezakiKurihamaOmaezaki14SaganosekiAtsumiKinuuraKashimaKinuura15TokyoYokkaichiKashimaSakaiShimotsu16Amagasaki-NATokyoWakayamaWakayamaYokkaichi17KashimaKinuuraShinguShimotsuShingu18OmaezakiKisarazuYokkaichiKomatsushimaKisarazu19ShimotsuSaganosekiShirashimaKinuuraWakayama20YokkaichiOsakaSakaiTakamatsuShirashimaTable 8
Ratios of flows between Japan and the world.
Maritime networkFseqFvisitFweightFlowFJ=F∗NJapan,Nworld3020537196656141.37808E + 11FX=F∗NJapan,N¯Japan872595217200050185931561FW=F∗Nworld,Nworld377863213908291443.89796E + 12Ratio (%)FX/FJ28.8911.0436.42FX/FW2.310.561.29


## 5.6. Ranking Ports by Trading, Connection, and Centralities

Using the global connection data of the Japanese ports, we rank the ports, as shown in Table7. Kobe is the first grade.The Japanese ports are not different in terms of ranking of their throughput (usingCdegreei in Section 3) and network impact (using Cpageranki in Section 3) (see Table 9).Table 9
Ranking the Japanese ports by degree and PageRank centralities.
ThroughputCdegreeiNetwork impactCpagerankiRankPortiRankPorti1Chiba1Chiba2Higashi-Harima2Higashi-Harima3Kobe3Kobe4Kawasaki4Kawasaki5Yokohama5Yokohama6Osaka6Osaka7Shingu7Shingu8Omaezaki8Omaezaki9Yura9Yura10Nagoya10Nagoya11Tokyo11Tokyo12Atsumi12Sakai13Sakai13Atsumi14Kashima14Kashima15Kurihama15Kurihama16Wakayama16Wakayama17Komatsushima17Komatsushima18Shimotsu18Shimotsu19Kinuura19Kinuura20Takamatsu20Takamatsu


## 5.7. Primary Maritime Flows with the Maritime Silk Road

As seen from the primary maritime flows between Japan (NJapan) and the MSR (NMSR) (Figure 9), China, Singapore, and Malaysia are the central import countries connected to Japan.Figure 9
Primary flows between the Japanese ports and the MSR.From the top 20 connections between Japan and MSR (Δ20NJapan,NMSR, Table 10), we can identify three essential stakeholders: Hong Kong, Singapore, and Malaysia along the MSR.Table 10
Top 20 connections between Japan and the MSR.
NoJapan port (i)RegionMSR port (j)Fseqi,jFvisiti,jFweighti,j1KobeSingaporeSingapore13457671994984202YokohamaSingaporeSingapore12952891823217873YuraSingaporeSingapore13343781654080504YokohamaHong KongHong Kong16752631541322555TokyoHong KongHong Kong16450381480663986ChibaSingaporeSingapore8430911448502617KawasakiSingaporeSingapore9150721436963928KobeHong KongHong Kong15751071406518909TokyoSingaporeSingapore133282511590435410KobeMalaysiaPengerang Terminal121279511276146811NagoyaSingaporeSingapore123364210987548512ChibaMalaysiaPengerang Terminal78164210377627313YuraMalaysiaPengerang Terminal108216410066239314Higashi-HarimaSingaporeSingapore8324989578199215YokohamaChinaChiwan15228509342519916KawasakiMalaysiaPengerang Terminal7825269290115917YuraHong KongHong Kong13831739102816118AtsumiSingaporeSingapore12826859033387119YokohamaMalaysiaPengerang Terminal11824598739569120ShanghaiJapanYokohama162470284396110Table11 indicates the ratios of flows between Japan (NJapan) and the MSR (NMSR); about 20% of vessel flows of Japanese international trade are directed to the MSR, while Japan contributes to the MSR by a tiny ratio (from 0.52% to 4.49%) of flows. It implies that although the BRI document has not mentioned Japan, Japan has high connectivity with the BRI at least by the MSR.Table 11
Ratios of flows between Japan and the Maritime Silk Road.
Maritime networkFseqFvisitFweightFlowFJ=F∗NJapan,Nworld3020537196656141.37808E + 11FX=F∗NJapan,NMSR566579156525031290144747FMSR=F∗NMSR,Nworld126273333017036892.64665E + 12Ratio (%)FX/FJ18.767.9622.71FX/FMSR4.490.521.18


## 5.8. Primary Maritime Flows with China

In the connections between Japan (NJapan) and China (NChina) (see Figure 10 and Table 12), Hong Kong, Shanghai, Ningbo, and Guangzhou play essential roles. Although the flows between Japan and China account for 4.59∼9.21% of Japan, while just 0.61∼3.44% of China (see Table 13).Figure 10
Primary flows between Japan and China.Table 12
Top 20 connections between Japan and China.
NoChinese port (i)Japanese port (j)Fseqi,jFvisiti,jFweighti,j1Hong KongYokohama16752631541322552Hong KongTokyo16450381480663983Hong KongKobe15751071406518904ChiwanYokohama1522850934251995Hong KongYura1383173910281616ShanghaiYokohama1624702843961107Hong KongNagoya1353242839807158YangshanYokohama621000757359769Hong KongOsaka14734597261730810ShanghaiKobe18254587178672311ShanghaiTokyo16838097110255012ChiwanTokyo15526946638258513NingboYokohama9516166564457214ChiwanKobe14026086402011215QingdaoYokohama12821246351899716GuangzhouYokohama17518435563671817Hong KongAtsumi14922805543741618ShanghaiOsaka18738045331536619YantianYokohama938375078354020ShanghaiKawasaki152344750111425269 Chinese ports149 Japanese portsTable 13
Ratios of flows between China and Japan.
Maritime networkFseqFvisitFweightFlowFJ=F∗NJapan,Nworld3020537196656141.37808E + 11FX=F∗NJapan,NChina27831190265312468012503FChina=F∗NChina,Nworld80839202849735372.05516E + 12Ratio (%)FX/FJ9.214.599.05FX/FChina3.440.320.61


## 6. Discussion

Maritime networks are complex because they are agents of various stakeholders (port operators, ship operators, carriers, local port authorities and hinterlands, and multilevel governments). A port’s structure and behaviors are results of games among these stakeholders, while the maritime network in a country or region is a holistic emergency upon them. The real-world global maritime network consists of more than 6000 ports belonging to more than 200 economic entities. In the background of the maritime network, a lot of companies, organizations, and governments are involved. Their demands and benefits make the network alive and complicated in its structure and behaviors. The maritime networks are typically adaptive and complex, which indicates that no entity controls the network, or such control is finally impossible. The maritime network is a representative of related stakeholders. For example, a maritime network of the ports of a country delegates the benefits and powers of the country. Therefore, we use the maritime network to analyze the relations and behaviors of the stakeholders.Some studies formulated the maritime ports a maritime network by methods in network sciences (see Table1). The ports interconnect with each other by shipping liners or vessel movements. Mainly, centrality-based methods are used to reveal the port significances in the network and impacts on the network. Network-based statistics help reveal network-level structures and behaviors [1]. The pioneering studies seldom investigate the countries or regional port systems in the global maritime network by data-driven methods due to that constructing large-scale or global maritime networks is challenging. This article results in the linkage between the maritime network and the country-level stakeholders in the context of the global maritime network.Geographically, Japan is isolated from the land covered by the BRI and MSR while it has many connections with China, Asia, and Eurasia by seaborne trades. In the results presented in Section5, although Japanese ports account for less vessel flows in the global maritime system, the interaction flow between Japan and China (also the MSR) is prominent when comparing the overall flows of Japan while it is just a small portion of the flows of China and MSR. The study provides enough reasons for Japan considering the essential connections with the MSR and Eurasia. In Section 3, the network definitions and analysis tools are formulated corresponding to a series of quantitative computing methods by extending the concepts and algorithms in network sciences. We take Japan, China, MSR, and the world maritime system as typical maritime networks here, and so we can analyze the interactions among the maritime networks of various countries or independent economies embedded in a global network in similar ways.


## 7. Conclusion

In this article, we addressed the research question: how do the maritime networks represent the country- and region-level interactions in the context of the global maritime network? We examined the interactions between Japan marine ports and the MSR by a data system and analysis tools. Japan connects with the MSR closely by seaborne transportation; a network of maritime networks contributes to the implications of interacted economical entities represented by the maritime networks, especially in the context of the global maritime network; prominent interactions among the maritime networks emerge by using the node- and edge-based network analysis tools. We construct a sample of a global maritime network with more than 6000 maritime ports to test and confirm the study. Although there are pioneering studies using methods in network sciences to investigate maritime networks (see Table1), this article is the first large-scale study to link country-level and regional level analysis and maritime networks upon a global maritime network.This study makes several scholarly contributions. It examines maritime network interactions embedded in a global maritime network, where the maritime networks are agents for country-level and regional level entities, e.g., Japan, China, MSR, and the world maritime system. Besides, it is a first ever study to examine the interactions through maritime ports and shipping between Japan and China (and MSR and the world) using a reliable method in association with AIS data. In particular, although most studies of maritime networks use data of container liner shipping as a base, this article uses a novel secondary dataset that captures the port and vessel profile data and the vessels’ global movement tracks (AIS). This comprehensive dataset reflects the diversification in empirical methods in the big data and artificial intelligence era [40]. While the ports and shipping data and the AIS data have been used extensively in transport and resource management areas, we developed definitions and tools for the data-driven maritime networks.There are limitations in the data and methods applied to this study. We construct the networks using the data of 2016, while the maritime system evolves in the economic and trade systems in recent years. To obtain a concise large-scale maritime network, we must process, repair, and synthesize by many steps. The data and its processing are expensive and time-consuming at the present stage of this study. The data system will finally provide benchmark datasets for maritime networks that will be assessable by academic communities. Therefore, the data chain is so long to guarantee and test the data quality. We focused on the application methods based on network sciences to constructed networks. However, the present developed analysis methods cannot handle the uncertainty, dynamics, and even random errors of the real-world maritime networks completely [41]. The stakeholders at the national and regional levels are complicated, and their observations and decisions must be affected by various sources of information. The maritime networks should integrate with various sources in holistic decision-making environments.Several future studies would be desirable. First, we can extend the proposed models to examine other economy-, policy-, and sustainability-related impacts of maritime network interactions on regional and global maritime networks. At the port, national, and regional levels, the impacts are different and mutually affected. It is beneficial to construct a multilayer network for studying the evolutionary behaviors of the networks of subnetworks [35, 42]. Second, we mainly extend the network presentation, generation, and necessary analyzing concepts and methods, which can be further verified and promoted in generalized networks, especially by coupling with methods in complex systems. Third, we use the maritime networks that are generated by a set of ports in the global maritime network. In the view of network structure, we may use community detection and clustering algorithms to develop self-adaptive and evolutionary maritime networks by using the developed data system. It may contribute to new algorithms in network analysis. In summary, this study is the start of studying the network of networks.



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*Source: 3769307-2020-05-15.xml*