Abstract
This paper examines how spatial distance affects network topology on empirical data concerning the Global Container Shipping Network (GCSN). The GCSN decomposes into 32 multiplex layers, defined at several spatial levels, by successively removing connections of smaller distances. This multilayer decomposition approach allows studying the topological properties of each layer as a function of distance. The analysis provides insights into the hierarchical structure and (importing and exporting) trade functionality of the GCSN, hub connectivity, several topological aspects, and the distinct role of China in the network’s structure. It also shows that bidirectional links decrease with distance, highlighting the importance of asymmetric functionality in carriers’ operations. It further configures six novel clusters of ports concerning their spatial coverage. Finally, it reveals three levels of geographical scale in the structure of GCSN (where the network topology significantly changes): the neighborhood (local connectivity); the scale of international connectivity (mesoscale or middle connectivity); and the intercontinental market (large scale connectivity). The overall approach provides a methodological framework for analyzing network topology as a function of distance, highlights the spatial dimension in complex and multilayer networks, and provides insights into the spatial structure of the GCSN, which is the most important market of the global maritime economy.
Highlights
Spatial networks, and their underlying socioeconomic structures, are described by a symbiotic relation: on the one hand, networks facilitate trade and other socioeconomic interactions supporting regional and economic development[1,2]; on the other hand, the derived demand in the associated regional markets supports the development process of spatial and transportation networks, which are structures of considerable sunk costs affecting the future developmental dynamics of the spatial units participating in these n etworks[1]
Maritime n etworks[18] can display different properties than land transportation networks and overcome planarity due to their attribute to conduct transportation on the sea surface instead of line infrastructure channels. This structural property is reflected[3,7,18,19,20,21,22,23] on (a) higher average degree than land transportation networks, (b) much larger average clustering coefficient than of counterpart lattices, and (c) degree distributions described by power-law patterns that often are typical of standard non-spatial networks
Airline networks are non-planar spatial networks, privileged to conduct transportation in the 3d-space instead of line infrastructure channels. This property reflects o n3,7,27–33 (a) the shape of the degree distribution, which fits power-law curves and is heavy-tailed with a cutoff, due to the physical constraints on the maximum number of connections that a single airport can handle; (b) the average path length, which is smaller than of counterpart lattices; (c) the significant correlations between topology and geography, implying that larger airports have connections with higher traffic and more distant connections; (d) the high clustering, which is slightly decreasing at large degrees (k), illustrating the role of large airports that provide non-stop connections to different not interconnected regions; (e) and a clique-like configuration, because large weights concentrate on links between large airports
Summary
Their underlying socioeconomic structures, are described by a symbiotic relation: on the one hand, networks facilitate trade and other socioeconomic interactions supporting regional and economic development[1,2]; on the other hand, the derived demand in the associated regional markets supports the development process of spatial and transportation networks, which are structures of considerable sunk costs affecting the future developmental dynamics of the spatial units participating in these n etworks[1]. Economists and regional scientists tend to conceptualize space in econometric terms and to manage the spatial dimension either as a separate econometric variable or through a given cost or facilitation (such as trade cost, tariff, and time); geographers, engineers, and spatial planners consider space as geospatial information expressed by geographical coordinates and territorial attributes (such as port city population, socioeconomic features, etc.); while physicists and mathematicians analyze the topological differences captured before and after the networks embedding in metric s paces[2,6] Despite this polyphony, it is possible to synthesize the literature on spatial networks and related constraints as follows[2,3,6,33]: (a) through the examination of the shape of degree distribution, where a bell-shaped configuration peaked around the average degree implies the effect of planarity in the configuration of network topology; (b) in reference to theoretical (null) graph models, according to which topological aspects and measures of real-world or other empirical networks are compared with the results of counterpart null models of lattice-like, random-like, ring-like, smallworld, hub-and-spoke, and other known topologies; (c) sometimes through spectral pattern recognition based on the sparsity (spy plot) patterns of the adjacency and connectivity matrices of spatial networks, and (d) by examining correlations between the measure of degree and the betweenness centrality (i.e. network intermediacy) and strength (i.e. traffic volume), to detect whether hubs (i.e. nodes of high connectivity) intermediate to the majority of paths and undertake the highest traffic load
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