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      Multiscale core-periphery structure in a global liner shipping network

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          Abstract

          Maritime transport accounts for a majority of trades in volume, of which 70% in value is carried by container ships that transit regular routes on fixed schedules in the ocean. In the present paper, we analyse a data set of global liner shipping as a network of ports. In particular, we construct the network of the ports as the one-mode projection of a bipartite network composed of ports and ship routes. Like other transportation networks, global liner shipping networks may have core-periphery structure, where a core and a periphery are groups of densely and sparsely interconnected nodes, respectively. Core-periphery structure may have practical implications for understanding the robustness, efficiency and uneven development of international transportation systems. We develop an algorithm to detect core-periphery pairs in a network, which allows one to find core and peripheral nodes on different scales and uses a configuration model that accounts for the fact that the network is obtained by the one-mode projection of a bipartite network. We also found that most ports are core (as opposed to peripheral) ports and that ports in some countries in Europe, America and Asia belong to a global core-periphery pair across different scales, whereas ports in other countries do not.

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          Finding and evaluating community structure in networks

          We propose and study a set of algorithms for discovering community structure in networks -- natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative removal of edges from the network to split it into communities, the edges removed being identified using one of a number of possible "betweenness" measures, and second, these measures are, crucially, recalculated after each removal. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems.
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            Fast unfolding of communities in large networks

            We propose a simple method to extract the community structure of large networks. Our method is a heuristic method that is based on modularity optimization. It is shown to outperform all other known community detection method in terms of computation time. Moreover, the quality of the communities detected is very good, as measured by the so-called modularity. This is shown first by identifying language communities in a Belgian mobile phone network of 2.6 million customers and by analyzing a web graph of 118 million nodes and more than one billion links. The accuracy of our algorithm is also verified on ad-hoc modular networks. .
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              Functional cartography of complex metabolic networks

              , (2005)
              High-throughput techniques are leading to an explosive growth in the size of biological databases and creating the opportunity to revolutionize our understanding of life and disease. Interpretation of these data remains, however, a major scientific challenge. Here, we propose a methodology that enables us to extract and display information contained in complex networks. Specifically, we demonstrate that one can (i) find functional modules in complex networks, and (ii) classify nodes into universal roles according to their pattern of intra- and inter-module connections. The method thus yields a ``cartographic representation'' of complex networks. Metabolic networks are among the most challenging biological networks and, arguably, the ones with more potential for immediate applicability. We use our method to analyze the metabolic networks of twelve organisms from three different super-kingdoms. We find that, typically, 80% of the nodes are only connected to other nodes within their respective modules, and that nodes with different roles are affected by different evolutionary constraints and pressures. Remarkably, we find that low-degree metabolites that connect different modules are more conserved than hubs whose links are mostly within a single module.
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                Author and article information

                Contributors
                naoki.masuda@bristol.ac.uk
                Journal
                Sci Rep
                Sci Rep
                Scientific Reports
                Nature Publishing Group UK (London )
                2045-2322
                23 January 2019
                23 January 2019
                2019
                : 9
                : 404
                Affiliations
                [1 ]ISNI 0000 0004 1754 9200, GRID grid.419082.6, CREST, JST, Kawaguchi Center Building, 4-1-8, Honcho, ; Kawaguchi-shi, Saitama 332-0012 Japan
                [2 ]ISNI 0000 0004 1936 7603, GRID grid.5337.2, Department of Engineering Mathematics, Merchant Venturers Building, , University of Bristol, ; Woodland Road, Clifton, Bristol BS8 1UB United Kingdom
                [3 ]ISNI 0000 0000 9247 7930, GRID grid.30055.33, Faculty of Management and Economics, Dalian University of Technology, ; No. 2 Linggong Road, Ganjingzi District, Dalian City, Liaoning Province 116024 China
                Author information
                http://orcid.org/0000-0002-9414-6814
                http://orcid.org/0000-0001-5737-1214
                http://orcid.org/0000-0003-1567-801X
                Article
                35922
                10.1038/s41598-018-35922-2
                6344524
                30674915
                16f994b1-58d9-4868-acea-13ffa59c9ebc
                © The Author(s) 2019

                Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

                History
                : 16 August 2018
                : 5 November 2018
                Funding
                Funded by: FundRef https://doi.org/10.13039/501100002858, China Postdoctoral Science Foundation;
                Award ID: 2017M621141
                Award Recipient :
                Funded by: FundRef https://doi.org/10.13039/501100001809, National Natural Science Foundation of China (National Science Foundation of China);
                Award ID: 71371040
                Award ID: 71871042
                Award Recipient :
                Funded by: FundRef https://doi.org/10.13039/501100003382, JST | Core Research for Evolutional Science and Technology (CREST);
                Award ID: JPMJCR1304
                Award Recipient :
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