Multi-Scale Higher-Order Dependencies (MSHOD): Higher-Order Interactions Mining and Key Nodes Identification for Global Liner Shipping Network
<p>Schematic of higher-order Markov properties in GLSRFs.</p> "> Figure 2
<p>BuildMSHODN algorithm. There are three steps in the algorithm: the extraction of higher-order dependency rules, edge reconfiguration, and the construction of higher-order dependency networks with multi-scale attributes.</p> "> Figure 3
<p>Correspondence between higher-order nodes and physical nodes.</p> "> Figure 4
<p>(<b>a</b>) SSFODN and (<b>b</b>) SSHODN (using part of Singapore’s connectivity as an example).</p> "> Figure 5
<p>Example of second-order dependency relationships in the SSHODN. (<b>a</b>–<b>d</b>) Nodes on either side representing paths with dependency relationships using Singapore (port) as the hub node (<math display="inline"><semantics> <mrow> <mi>n</mi> <mi>s</mi> <mi>d</mi> <mi>p</mi> <mi>h</mi> <mo>−</mo> <mi>S</mi> <mi>i</mi> <mi>n</mi> <mi>g</mi> <mi>a</mi> <mi>p</mi> <mi>o</mi> <mi>r</mi> <mi>e</mi> </mrow> </semantics></math>). The percentage on the left node indicates the proportion of <math display="inline"><semantics> <mrow> <mi>n</mi> <mi>s</mi> <mi>d</mi> <mi>p</mi> <mi>h</mi> <mi>s</mi> <mi>h</mi> <mo>−</mo> <mi>y</mi> <mo>−</mo> <mi>x</mi> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mi>n</mi> <mi>s</mi> <mi>d</mi> <mi>p</mi> <mi>h</mi> <mo>−</mo> <mi>x</mi> </mrow> </semantics></math>. The percentage on the right node indicates the proportion of <math display="inline"><semantics> <mrow> <mi>n</mi> <mi>s</mi> <mi>d</mi> <mi>p</mi> <mi>h</mi> <mi>s</mi> <mi>h</mi> <mi>r</mi> <mo>−</mo> <mi>y</mi> <mo>−</mo> <mi>x</mi> <mo>−</mo> <mi>z</mi> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mi>n</mi> <mi>s</mi> <mi>d</mi> <mi>p</mi> <mi>h</mi> <mi>s</mi> <mi>h</mi> <mo>−</mo> <mi>y</mi> <mo>−</mo> <mi>x</mi> </mrow> </semantics></math>.</p> "> Figure 6
<p>Example illustrating the importance of higher-order interactions in problem analysis.</p> "> Figure 7
<p>Third-order dependency relationships in SSHODN (using Shanghai as an example). (<b>a</b>–<b>d</b>) represent the nodes corresponding to the respective container ports.</p> "> Figure 8
<p><math display="inline"><semantics> <mo>Θ</mo> </semantics></math> and <math display="inline"><semantics> <mover accent="true"> <mo>Θ</mo> <mo>˜</mo> </mover> </semantics></math> results for the top 20 container ports by global average annual throughput. (<b>a</b>,<b>b</b>) The results of analyzing different ports using <math display="inline"><semantics> <mo>Θ</mo> </semantics></math> and <math display="inline"><semantics> <mover accent="true"> <mo>Θ</mo> <mo>˜</mo> </mover> </semantics></math>, respectively, where gray bars represent <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>T</mi> <mi>P</mi> </mrow> </semantics></math>, green bars represent <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>n</mi> <mi>o</mi> <mi>t</mi> <mi>T</mi> </mrow> </semantics></math>, and pink lines indicate whether <math display="inline"><semantics> <mo>Θ</mo> </semantics></math> (<math display="inline"><semantics> <mover accent="true"> <mo>Θ</mo> <mo>˜</mo> </mover> </semantics></math>) is among the top 20. (<b>c</b>) The results of <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mo>Θ</mo> </mrow> </semantics></math> for the ports with the top 20 annual average throughputs.</p> "> Figure 9
<p>Key nodes identification results using the SSHODN in GLSRFs. (<b>a</b>,<b>b</b>) The container ports with the largest changes in <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mo>Θ</mo> <mo>></mo> <mn>0</mn> </mrow> </semantics></math> (circles) and <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mo>Θ</mo> <mo><</mo> <mn>0</mn> </mrow> </semantics></math> (stars), excluding the top 20 by annual throughput. Different colors represent different geographical regions, and the size of the shapes indicates the magnitude of <math display="inline"><semantics> <mrow> <mo>|</mo> <mo>Δ</mo> <mo>Θ</mo> <mo>|</mo> </mrow> </semantics></math>. (<b>b</b>) Dashed ellipse highlighting a zoomed-in section near Oceania. For more details, see <a href="#jmse-12-01305-t003" class="html-table">Table 3</a>.</p> "> Figure 10
<p>Example of second-order relationships in the ISHODN. (<b>a</b>–<b>d</b>) Nodes on either side representing paths with dependency relationships using Singapore (country) as the hub node (<math display="inline"><semantics> <mrow> <mi>n</mi> <mi>s</mi> <mi>d</mi> <mi>p</mi> <mi>h</mi> <mo>−</mo> <mi>S</mi> <mi>i</mi> <mi>n</mi> <mi>g</mi> <mi>a</mi> <mi>p</mi> <mi>o</mi> <mi>r</mi> <mi>e</mi> </mrow> </semantics></math>). The percentages on the left side of the nodes indicate the proportion of <math display="inline"><semantics> <mrow> <mi>n</mi> <mi>s</mi> <mi>d</mi> <mi>p</mi> <mi>h</mi> <mi>s</mi> <mi>h</mi> <mo>−</mo> <mi>y</mi> <mo>−</mo> <mi>x</mi> </mrow> </semantics></math> in <math display="inline"><semantics> <mrow> <mi>n</mi> <mi>s</mi> <mi>d</mi> <mi>p</mi> <mi>h</mi> <mo>−</mo> <mi>x</mi> </mrow> </semantics></math>. The percentages on the right side of the nodes represent the proportion of <math display="inline"><semantics> <mrow> <mi>n</mi> <mi>s</mi> <mi>d</mi> <mi>p</mi> <mi>h</mi> <mi>s</mi> <mi>h</mi> <mi>r</mi> <mo>−</mo> <mi>y</mi> <mo>−</mo> <mi>x</mi> <mo>−</mo> <mi>z</mi> </mrow> </semantics></math> in <math display="inline"><semantics> <mrow> <mi>n</mi> <mi>s</mi> <mi>d</mi> <mi>p</mi> <mi>h</mi> <mi>s</mi> <mi>h</mi> <mo>−</mo> <mi>y</mi> <mo>−</mo> <mi>x</mi> </mrow> </semantics></math>.</p> "> Figure 11
<p>Third-order and fourth-order dependency relationships in the ISHODN. (<b>a</b>,<b>b</b>) The four or five columns of nodes represent different countries. Different colors signify the extracted dependency paths, with (<b>a</b>) highlighted in blue representing <math display="inline"><semantics> <mrow> <mi>t</mi> <mi>d</mi> <mi>p</mi> <mi>o</mi> <mo>−</mo> <mi>C</mi> <mi>h</mi> <mi>i</mi> <mi>n</mi> <mi>a</mi> </mrow> </semantics></math>.</p> "> Figure 12
<p>Key nodes identification results using ISHODN the GLSRF. (<b>a</b>–<b>d</b>) Yellow bars representing <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mo>Υ</mo> </mrow> </semantics></math>, blue circles for <math display="inline"><semantics> <mo>Υ</mo> </semantics></math>, and pink stars for <math display="inline"><semantics> <mover accent="true"> <mo>Υ</mo> <mo>˜</mo> </mover> </semantics></math>. Each subplot has a left y-axis showing the percentage values for <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mo>Υ</mo> </mrow> </semantics></math> and a right y-axis for the values of <math display="inline"><semantics> <mo>Υ</mo> </semantics></math> or <math display="inline"><semantics> <mover accent="true"> <mo>Υ</mo> <mo>˜</mo> </mover> </semantics></math>. (<b>a</b>) The top 10 countries or regions with the highest <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mo>Υ</mo> <mo>></mo> <mn>0</mn> </mrow> </semantics></math>. (<b>b</b>) The bottom 10 countries or regions with <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mo>Υ</mo> <mo><</mo> <mn>0</mn> </mrow> </semantics></math>. (<b>c</b>,<b>d</b>) Mainly Southeast Asia, Oceania, and other representative results.</p> "> Figure 13
<p>The evolution of <math display="inline"><semantics> <mover accent="true"> <mo>Υ</mo> <mo>˜</mo> </mover> </semantics></math> across various years. (<b>a</b>–<b>c</b>) Heat maps of <math display="inline"><semantics> <mover accent="true"> <mo>Υ</mo> <mo>˜</mo> </mover> </semantics></math> for various countries within GLSN for the years 2018, 2020, and 2023, respectively. Countries or regions colored grey indicate a <math display="inline"><semantics> <mover accent="true"> <mo>Υ</mo> <mo>˜</mo> </mover> </semantics></math> value of 0 for the corresponding year, meaning they were not covered in GLSRF. The intensity of the colors in the heat maps reflects the degree of dependency of the countries in GLSN, with <math display="inline"><semantics> <mover accent="true"> <mo>Υ</mo> <mo>˜</mo> </mover> </semantics></math> values ranging from <math display="inline"><semantics> <mrow> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>0.02</mn> <mo>]</mo> </mrow> </semantics></math>. The x-axes in (<b>d</b>,<b>e</b>) represent different years, while the y-axes show the values of <math display="inline"><semantics> <mover accent="true"> <mo>Υ</mo> <mo>˜</mo> </mover> </semantics></math>. (<b>d</b>) The <math display="inline"><semantics> <mover accent="true"> <mo>Υ</mo> <mo>˜</mo> </mover> </semantics></math> values for traditionally maritime developed countries. (<b>e</b>) Data for a selection of representative countries.</p> "> Figure 14
<p>Key nodes identification results using the LSHODN in GLSRFs. (<b>a</b>) The geographical distribution of seven different organizations. (<b>b</b>) The results of key nodes identification, where pink represents <math display="inline"><semantics> <mo>Θ</mo> </semantics></math> and blue represents <math display="inline"><semantics> <mover accent="true"> <mo>Θ</mo> <mo>˜</mo> </mover> </semantics></math>.</p> ">
Abstract
:1. Introduction
2. Materials and Methods
2.1. The Higher-Order Markov Properties in GLSRFs
2.2. Construction of the MSHODN
Algorithm 1 Build MSHODN and MSFODN |
|
2.3. The Method for Identifying Key Nodes within MSHODN
Algorithm 2 Method for key nodes identification in MSFODN and MSHODN |
|
3. Experiments and Analysis
3.1. Dataset
3.2. Experiment Design
4. Results
4.1. Small-Scale Experiments on GLSRF
4.2. Intermediate-Scale Experiments on GLSRF
Large-Scale Experiments on GLSRF
4.3. Further Discussion
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Table of the Top 20 Global Container Ports by Annual Throughput
Ports | TEU | Ports | TEU |
---|---|---|---|
Shanghai | 47.3 | Singapore | 37.3 |
Ningbo-Zhoushan | 33.4 | Shenzhen | 30.0 |
Qingdao | 25.7 | Guangzhou | 24.6 |
Busan | 22.1 | Tianjin | 21.0 |
Los Angeles/Long Beach | 19.0 | Hong Kong | 16.6 |
Rotterdam | 14.5 | Dubai/Jebel Ali | 14.0 |
Antwerp-Bruges | 13.5 | Kelang | 13.2 |
Xiamen | 12.4 | Tanjung Priok Port | 10.5 |
Kaohsiung | 9.5 | New York/New Jersey | 9.5 |
Laem Chabang | 8.7 | Hamburg | 8.4 |
Appendix B. Table of Changes in ΔΘ for Oceania
Ports | Ports | ||||||
---|---|---|---|---|---|---|---|
Adelaide | 0.00066 | 0.00060 | −9.31% | Brisbane | 0.00196 | 0.00167 | −14.67% |
Botany Bay | 0.00257 | 0.00214 | −16.72% | Lyttelton | 0.00100 | 0.00067 | −32.96% |
Wellington | 0.00069 | 0.00041 | −41.18% | Fremantle | 0.00119 | 0.00067 | −43.31% |
Tauranga | 0.00248 | 0.00139 | −43.81% | Auckland | 0.00235 | 0.00127 | −46.09% |
Moresby | 0.00068 | 0.00036 | −47.15% | Napier | 0.00085 | 0.00044 | −48.43% |
Nelson | 0.00106 | 0.00049 | −53.62% | Bluff | 0.00039 | 0.00017 | −56.51% |
Lae | 0.00122 | 0.00050 | −58.98% | Townsville | 0.00040 | 0.00014 | −64.53% |
Chalmers | 0.00078 | 0.00023 | −70.61% | Georgetown | 0.00037 | 0.00011 | −70.70% |
Apia | 0.00090 | 0.00026 | −71.34% | Marsden Point | 0.00059 | 0.00017 | −71.60% |
Suva | 0.00074 | 0.00020 | −73.09% | Nuku’alofa | 0.00051 | 0.00013 | −73.40% |
Lautoka | 0.00120 | 0.00026 | −78.26% | Kimbe | 0.00038 | 0.00008 | −78.71% |
Darwin | 0.00039 | 0.00008 | −80.45% | Timaru | 0.00074 | 0.00014 | −81.53% |
Honiara | 0.00076 | 0.00014 | −82.07% | Vila | 0.00091 | 0.00015 | −83.95% |
Newcastle | 0.00031 | 0.00004 | −87.76% | Esperance | 0.00053 | 0.00005 | −89.74% |
Majuro | 0.00075 | 0.00008 | −89.96% | Koror | 0.00077 | 0.00006 | −92.08% |
Appendix C. Table of Major Global Economic Organizations
Complete Names and Abbreviations of Each Organization | List of Included Countries |
---|---|
North American Free Trade Agreement (NAFTA) | United States, Canada, Mexico. |
European Union (EU) | Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden. |
China-Japan-South Korea Cooperation (CJK) | China, Japan, South Korea. |
Association of Southeast Asian Nations (ASEAN) | Indonesia, Malaysia, Philippines, Singapore, Thailand, Vietnam, Myanmar, Cambodia, Laos, Brunei. |
Southern Common Market (Mercosur) | Argentina, Brazil, Paraguay, Uruguay. |
Southern African Development Community (SADC) | Angola, Botswana, Comoros, Democratic Republic of the Congo, Eswatini, Lesotho, Madagascar, Malawi, Mauritius, Mozambique, Namibia, Seychelles, South Africa, Tanzania, Zambia, Zimbabwe. |
Middle East and North Africa (MENA) | Algeria, Bahrain, Djibouti, Egypt, Iran, Iraq, Israel, Jordan, Kuwait, Lebanon, Libya, Malta, Morocco, Oman, Qatar, Saudi Arabia, Syria, Tunisia, United Arab Emirates, Palestine, Yemen. |
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Indicators | SSFODN | SSHODN |
---|---|---|
Number of nodes | 700 | 1411 |
Number of edges | 10,170 | 15,273 |
Average Degree | 14.529 | 10.824 |
Diameter of network | 7 | 12 |
Average Path length | 3.095 | 3.555 |
Graph Density | 0.021 | 0.008 |
Number of Weakly Connected Components | 1 | 1 |
Number of Strongly Connected Components | 13 | 24 |
Average Clustering Coefficient | 0.479 | 0.269 |
Meaning | Abbreviation |
---|---|
The number of second-order dependent paths with node x as the hub. | |
The number of second-order dependent paths starting from y with node x as the hub. | |
The number of second-order dependent paths starting from y, using node x as the hub, and reaching z. | |
The third-order dependent paths originating from x. | |
The third-order dependent paths with x as the second step. | |
The third-order dependent paths with x as the third step. | |
The third-order dependent paths with x as the fourth step. | |
Ports ranked in the top 20 by both throughput and (). | |
Ports ranked in the top 20 by throughput but not by (). | |
Ports ranked in the top 20 by () but not by throughput. |
Ports | Ports | ||||||
---|---|---|---|---|---|---|---|
Foshan | 0.001865 | 0.010873 | 482.98% | Tampico | 0.0004801 | 0.0000063 | −98.69% |
Taicang | 0.004562 | 0.019372 | 324.6% | Amamapare | 0.0002671 | 0.0000047 | −98.22% |
Kobe | 0.004051 | 0.008472 | 109.14% | El Guamache | 0.0002152 | 0.0000044 | −97.95% |
Osaka | 0.003471 | 0.007236 | 108.46% | Meppel | 0.0002152 | 0.0000044 | −97.95% |
Haiphong | 0.003492 | 0.005783 | 65.61% | Oxelösund | 0.0002152 | 0.0000044 | −97.95% |
Bangkok | 0.002503 | 0.004073 | 62.73% | Valletta | 0.0002152 | 0.0000044 | −97.95% |
Auckland | 0.001284 | 0.001993 | 55.23% | Funakoshi Ko | 0.0002152 | 0.0000044 | −97.95% |
Santos | 0.003013 | 0.003969 | 31.71% | Sibu | 0.0002152 | 0.0000044 | −97.95% |
Ashdod | 0.002499 | 0.003250 | 30.04% | Manatee | 0.0006233 | 0.0000141 | −97.73% |
Valencia | 0.005550 | 0.007009 | 26.29% | Algiers | 0.0003026 | 0.0000070 | −97.69% |
Piraeus | 0.005790 | 0.007261 | 25.4% | Nanchang | 0.0002987 | 0.0000086 | −97.11% |
Iskenderun | 0.001284 | 0.001578 | 22.85% | Kampen | 0.0003324 | 0.0000107 | −96.79% |
Montoir | 0.000699 | 0.000833 | 19.25% | Ilo | 0.0002626 | 0.0000096 | −96.36% |
Abidjan | 0.000805 | 0.000955 | 18.7% | Esmeraldas | 0.0002830 | 0.0000117 | −95.85% |
Gothenburg | 0.001341 | 0.001580 | 17.91% | Sundsvall | 0.0003565 | 0.0000199 | −94.42% |
Charleston | 0.001743 | 0.001974 | 13.26% | Halmstad | 0.0003324 | 0.0000204 | −93.86% |
Klaipeda | 0.001971 | 0.002210 | 12.13% | Bahía Blanca | 0.0007225 | 0.0000463 | −93.59% |
Leixoes | 0.002458 | 0.002714 | 10.4% | Salem | 0.0005450 | 0.0000362 | −93.63% |
Balboa | 0.002792 | 0.003066 | 9.8% | Antsiranana | 0.0004019 | 0.0000291 | −92.77% |
Melbourne | 0.001779 | 0.001802 | 1.27% | Oceania 1 |
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Fu, Y.; Li, X.; Li, J.; Yu, M.; Lu, X.; Huangpeng, Q.; Duan, X. Multi-Scale Higher-Order Dependencies (MSHOD): Higher-Order Interactions Mining and Key Nodes Identification for Global Liner Shipping Network. J. Mar. Sci. Eng. 2024, 12, 1305. https://doi.org/10.3390/jmse12081305
Fu Y, Li X, Li J, Yu M, Lu X, Huangpeng Q, Duan X. Multi-Scale Higher-Order Dependencies (MSHOD): Higher-Order Interactions Mining and Key Nodes Identification for Global Liner Shipping Network. Journal of Marine Science and Engineering. 2024; 12(8):1305. https://doi.org/10.3390/jmse12081305
Chicago/Turabian StyleFu, Yude, Xiang Li, Jichao Li, Mengjun Yu, Xiongyi Lu, Qizi Huangpeng, and Xiaojun Duan. 2024. "Multi-Scale Higher-Order Dependencies (MSHOD): Higher-Order Interactions Mining and Key Nodes Identification for Global Liner Shipping Network" Journal of Marine Science and Engineering 12, no. 8: 1305. https://doi.org/10.3390/jmse12081305