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We propose a novel approach to the study of international trade based on a theory of country integration that embodies a broad systemic viewpoint on the relationship between trade and growth. Our model leads to an indicator of country openness that measures a country's level of integration through the full architecture of its connections in the trade network. We apply our methodology to a sample of 204 countries and find a sizable and significant positive relationship between our integration measure and a country's growth rate, while that of the traditional measures of outward orientation is only minor and statistically insignificant.