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Marine transportation is pivotal in the rapid development of global trade, significantly enhancing international economic and trade connectivity and impacting the sustainable development of the global economy. In this study, we developed a novel technical framework based on the Laplacian matrix to evaluate the node significance and edge connectivity of the global shipping network using 2019 vessel schedule data from the top 30 liner shipping companies, as ranked by Alphaliner. Our analyses were conducted in both L-space, characterizing the connectivity function, and P-space, characterizing the transfer function. The findings indicate the following. (1) There is no consistent relationship between node significance and centrality for most ports. Ports with high node significance are mainly located in the Asia–Pacific region, with Singapore Port being the port with the highest node significance in L-space and Shanghai Port being the port with the highest node significance in P-space. (2) In L-space, the structures with significant improvements in edge connectivity in the shipping network have at least one port node that exhibits both low degree centrality and low betweenness centrality; these are primarily found on East African routes. (3) In P-space, the structures with significant improvements in edge connectivity in the shipping network are more complex but are notably linked to the ports of Assaluyeh and Bandar Abbas in Iran. The proposed node evaluation and edge addition strategy effectively analyze port significance and edge connectivity, providing decision-making support for optimizing port layouts, supporting container route planning, and enhancing the overall performance of the shipping network. [ABSTRACT FROM AUTHOR]

Adolescence is a crucial period for physical and psychological development. The impact of negative life events represents a risk factor for the onset of neuropsychiatric disorders. This study aims to investigate the relationship between negative life events and structural brain connectivity, considering both graph theory and connectivity strength. A group (n = 487) of adolescents from the IMAGEN Consortium was divided into Low and High Stress groups. Brain networks were extracted at an individual level, based on morphological similarity between grey matter regions with regions defined using an atlas-based region of interest (ROI) approach. Between-group comparisons were performed with global and local graph theory measures in a range of sparsity levels. The analysis was also performed in a larger sample of adolescents (n = 976) to examine linear correlations between stress level and network measures. Connectivity strength differences were investigated with network-based statistics. Negative life events were not found to be a factor influencing global network measures at any sparsity level. At local network level, between-group differences were found in centrality measures of the left somato-motor network (a decrease of betweenness centrality was seen at sparsity 5%), of the bilateral central visual and the left dorsal attention network (increase of degree at sparsity 10% at sparsity 30% respectively). Network-based statistics analysis showed an increase in connectivity strength in the High stress group in edges connecting the dorsal attention, limbic and salience networks. This study suggests negative life events alone do not alter structural connectivity globally, but they are associated to connectivity properties in areas involved in emotion and attention.

[M. Ma, The connectivity of exchanged hypercubes, Discrete Math., Algorithms Appl. 2(2) (2010) 213–220.] proved that the vertex connectivity and the edge connectivity of the exchanged hypercube are each equal to the minimum degree of the graph. This paper presents a proof of that result, which is substantially simpler and more intuitive. [ABSTRACT FROM AUTHOR]

The problem of efficiently computing all k -edge-connected components (k -ECCs) of a graph G for a user-givenk has been extensively studied recently in view of its importance in many applications. The k -ECCs of G for all possible values ofk form a hierarchical structure; that is, any two different k -ECCs for the same k value are disjoint and any k -ECC is contained in a unique (k - 1) -ECC. In this paper, we study the problem of efficiently constructing the hierarchy tree of the k -ECCs for all possible k values, for a graph G. The existing approaches TD and BU construct the hierarchy tree in either a top-down manner or a bottom-up manner, with both having the time complexity of O (δ (G) × T KECC (G)) , where δ (G) is the degeneracy of G and T KECC (G) is the time complexity of computing all k -ECCs of G for a specific k value. Here, the degeneracy of G is defined as the maximum value among the minimum vertex degrees of all subgraphs of G and is at most m where m is the number of edges in G. To improve the time complexity, we propose a divide-and-conquer approach DC running in O ((log δ (G)) × T KECC (G)) time; this time complexity is optimal up to a logarithmic factor. However, a straightforward implementation of DC would take O ((m + n) log δ (G)) main-memory space, which could easily run out-of-memory when processing large graphs; here, n is the number of vertices in G. To reduce the main-memory footprint of our algorithm, we propose adjacency array-based techniques to optimize the space complexity to 2 m + O (n log δ (G)) and denote our resulting algorithm by DC - AA . As a by-product of DC - AA , we also improve the space complexity of the state-of-the-art algorithm for computing all k -ECCs for a specific k to 2 m + O (n) , by using the same technique as used in DC - AA . Finally, we propose optimization techniques to improve the practical efficiency of the existing approach BU and denote the space-optimized version of it as BU ∗ - AA which runs in O (δ (G) × T KECC (G)) time and 2 m + O (n) space. Extensive experiments on large real graphs and synthetic graphs demonstrate that our algorithms DC - AA and BU ∗ - AA outperform the state-of-the-art approaches by up to 28 times in terms of running time and by up to 8 times in terms of main memory usage. In particular, our approach BU ∗ - AA processes the Twitter graph, which has more than 1 billion undirected edges, in 29 min with 13.5 GB memory, while the state-of-the-art approaches take more than 13 h after our space optimization; note that the state-of-the-art approaches run out-of-memory if without our space optimization. Our empirical study also shows that BU ∗ - AA , despite having a higher time complexity, performs better than DC - AA in practice. We also remark that BU ∗ - AA is much simpler and easier to implement than DC - AA . [ABSTRACT FROM AUTHOR]

Marine transportation is pivotal in the rapid development of global trade, significantly enhancing international economic and trade connectivity and impacting the sustainable development of the global economy. In this study, we developed a novel technical framework based on the Laplacian matrix to evaluate the node significance and edge connectivity of the global shipping network using 2019 vessel schedule data from the top 30 liner shipping companies, as ranked by Alphaliner. Our analyses were conducted in both L-space, characterizing the connectivity function, and P-space, characterizing the transfer function. The findings indicate the following. (1) There is no consistent relationship between node significance and centrality for most ports. Ports with high node significance are mainly located in the Asia–Pacific region, with Singapore Port being the port with the highest node significance in L-space and Shanghai Port being the port with the highest node significance in P-space. (2) In L-space, the structures with significant improvements in edge connectivity in the shipping network have at least one port node that exhibits both low degree centrality and low betweenness centrality; these are primarily found on East African routes. (3) In P-space, the structures with significant improvements in edge connectivity in the shipping network are more complex but are notably linked to the ports of Assaluyeh and Bandar Abbas in Iran. The proposed node evaluation and edge addition strategy effectively analyze port significance and edge connectivity, providing decision-making support for optimizing port layouts, supporting container route planning, and enhancing the overall performance of the shipping network.

Edge connectivity is often used to capture edge fault tolerance. As for most common networks, their edge connectivity is exactly equal to their minimum degree. Edge matroidal connectivity and conditional edge matroidal connectivity are two new graph edge connectivity parameters that can be defined when a partition of the edge set is given, for example when the network is built with different kinds of edges having different expected faultiness. And those two edge connectivity parameters can measure edge fault tolerance more than the traditional definition. The edge matroidal connectivity is based on the associated edge partition and the other is a generalization called conditional edge matroidal connectivity. We analyze these new parameters on hypercubes and folded hypercubes which are well studied networks. In this study, we consider their standard dimensional partition of the edges. This study leads to more structural insights about edge connectivity and yields many interesting questions. • We propose two new edge connectivity parameters for a graph based on the associated edge partition. • The two edge connectivity parameters are edge matroidal connectivity and conditional edge matroidal connectivity. • We analyze the (conditional) edge matroidal connectivity for hypercubes and folded hypercubes. [ABSTRACT FROM AUTHOR]

Adolescence is a crucial period for physical and psychological development. The impact of negative life events represents a risk factor for the onset of neuropsychiatric disorders. This study aims to investigate the relationship between negative life events and structural brain connectivity, considering both graph theory and connectivity strength. A group (n = 487) of adolescents from the IMAGEN Consortium was divided into Low and High Stress groups. Brain networks were extracted at an individual level, based on morphological similarity between grey matter regions with regions defined using an atlas-based region of interest (ROI) approach. Between-group comparisons were performed with global and local graph theory measures in a range of sparsity levels. The analysis was also performed in a larger sample of adolescents (n = 976) to examine linear correlations between stress level and network measures. Connectivity strength differences were investigated with network-based statistics. Negative life events were not found to be a factor influencing global network measures at any sparsity level. At local network level, between-group differences were found in centrality measures of the left somato-motor network (a decrease of betweenness centrality was seen at sparsity 5%), of the bilateral central visual and the left dorsal attention network (increase of degree at sparsity 10% at sparsity 30% respectively). Network-based statistics analysis showed an increase in connectivity strength in the High stress group in edges connecting the dorsal attention, limbic and salience networks. This study suggests negative life events alone do not alter structural connectivity globally, but they are associated to connectivity properties in areas involved in emotion and attention., Competing Interests: Dr. Banaschewski has served as an advisor or consultant to Actelion, Hexal Pharma,Bristol-Myers Squibb, Desitin Arzneimittel, Eli Lilly, Lundbeck, Medice, Neurim Pharmaceuticals, Novartis, Pfizer, and Shire, UCB, and Vifor Pharma; he has received conference attendance support, conference support, or speaking fees from Eli Lilly, Janssen McNeil, Medice, Novartis, and Shire, and UCB; and he is involved in clinical trials conducted by Eli Lilly, Novartis, and Shire and Viforpharma; he received royalities from Hogrefe, Kohlhammer, CIP Medien, Oxford University Press; the present work is unrelated to these relationships. Dr. Barker has received honoraria from General Electric Healthcare for teaching on scanner programming courses and acts as a consultant for IXICO. Dr. Poustka served in an advisory or consultancy role for Roche and Viforpharm and received speaker’s fee by Shire. She received royalties from Hogrefe, Kohlhammer and Schattauer. The present work is unrelated to the above grants and relationships. The other authors report no biomedical financial interests or potential conflicts of interest., (© 2024 The Authors.)