In this paper, we use the social network method to analyze the structure of the international carbon emission network, which provides new perspectives and research methods for the study of carbon emission relations among countries. Based on the association matrix of carbon emissions among countries, we specify weight matrices and embed them into the global vector auto-regression (GVAR) model, which makes a more accurate measurement of the relationship between economic growth and carbon emissions among countries, and deeply investigate the internal relationship between international economic growth and carbon emissions.　　Firstly, the structural characteristics of individuals in the carbon emission network are analyzed. The results show that in the international carbon emission network, developed economies have achieved carbon transfer through importing a large number of intermediate products, and their in-degree in the international carbon emission network is large. Comparatively, the BRIC countries and the emerging economies have received carbon imports from developed countries while exporting products, resulting in their high out-degree. Developed countries have achieved " products import and carbon export”, while developing countries have shown the characteristics of " products export and carbon import”. China has established a large number of production links with other countries through processing trade and other ways, and then the carbon emission links have been established and become increasingly close. In general, the centrality of developed economies is relatively stable in the international carbon emission network, while the degree of centrality in developing countries or emerging economies has increased significantly.　　Based on the network structure characteristic analysis of the international carbon emission matrix, we further explore the impacts of one country’s economic growth on other countries’ carbon emissions through the carbon emission network transmission from the perspective of network association. The results show that under the shock of China’s economic growth, the changes of carbon emissions of representative economies, except India, show inverted " U” shape characteristics. The economic growth of developed countries except Japan and BRIC countries has positive effects of inverted " U” type on China’s carbon emissions while the economic outputs of emerging economies exert " U” type negative impacts on the carbon emissions of China. The status of international industrial specialization and the structure of commodity exports can largely explain the shock differences of economic growth and carbon emissions between representative economies and China.