Fig. 7: Representation of the GLSN and its structural core in the hyperbolic space.

The color of the nodes corresponds to the modular communities. In (a), the nodes belonging to the structural core are highlighted with a thicker black border and the intra-core connections are marked in dark gray, whereas the other connections are in light gray. Names of the structural-core ports are indicated in (b). The detected gateway-hub structural-core is at the center of the hyperbolic layout. Nodes at the center of this layout are crucial to support the efficient navigability of a complex network⁵⁸. From a previous analysis we know that these nodes at the center have also larger TEU (as presented in Fig. 1d). This indicates that the gateway-hub structural core is indeed mainly composed by ports with larger TEU that are fundamental for efficient navigability of the network in transporting cargoes traded worldwide. Therefore, structural-core ports are important candidates to be associated with international trade (as we will analyse in the next section). In order to be sure that the hyperbolic representation is meaningful and the community separation is significantly and properly represented in the hyperbolic layout, we computed an index of angular separation of the communities (ASI)⁶¹ in respect to the worst scenario in which the nodes of each community are equidistantly distributed over the circumference. This index is in the range [0,1]: 0 indicates the worst case, and 1 indicates a case of perfect angular separation. For the provided embedding the ASI is 0.7, which represents a good angular separation of the communities in the embedding space and is statistically significant with a p-value < 0.001 (see Supplementary Fig. 4 for details on the statistical test).