Maritime connectivity poses a challenge for the development of ports and global maritime trade. This issue, studied since the early 21st century, has gained increasing importance, to the point where UNCTAD has established several indices evaluating the maritime connectivity of countries and ports. To understand port dynamics and the role of maritime connectivity in local development, this article analyzes port connectivity in the global context of the world container shipping network using network theory. By decomposing the Port Liner Shipping Connectivity Index (PLSCI), we analyze for the years 2007 and 2016 the role of each component: the number of ships, the deployed capacity, the number of services, the number of companies, the maximum ship size, and the number of direct connections relative to the global maritime transport network. Then, we integrate a geographical dimension by introducing a connectivity variable based on distance, starting from the hypothesis that there is not only one form of connectivity but several depending on the distance of exchanges. Our results show that some ports with high overall connectivity scores do not achieve high scores in all our categories, and vice versa. This analysis clearly underlines that connectivity cannot be simply considered as a global indicator.