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The Canary Islands' economy is extremely dependent on sea transport. Since accessibility and connectivity are major determinants of international transport costs, the analysis of their main ports' connectivity is crucial for keeping costs under control. Since different port authorities manage the major ports of the Canary Islands, they could be tempted to compete for transshipment cargoes, instead of working together to facilitate supply chain integration that would increase their competitive standing. The aim of the paper is twofold. First, the infrastructure and superstructure endowment of the main Canarian ports and their accessibility, by evaluating site and situation factors, is documented. Secondly, the connectivity of the main Canarian ports is assessed by means of graph theory. This provides important measures that define a port's competitiveness, and its potential to achieve or keep regional or global hub status, and also to follow its evolution. A brief review of papers measuring port connectivity based on graph theory is included to illustrate the current approaches in port network analysis, and to justify our methodological framework. A sub-network of 53 ports directly related with Las Palmas and Tenerife ports has been selected for this purpose. Our findings are mainly related to the connections among the nodes in the sample network, and to the position that the targeted ports hold. Additionally, some policy recommendations, regarding how to improve the connectivity and competitiveness of the Canarian ports, are also enumerated. Previous analysis indicates that, at present, the Las Palmas port is the only regional hub in the Canaries. Both Canarian port authorities should differentiate themselves by specializing in certain valued added services and increasing traffic in these services. This would avoid the danger of a destructive competition between them to attract transit traffic. In summary they should be proactive in maintaining and improving the main Canarian ports' connectivity. [ABSTRACT FROM AUTHOR]