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.