Global climate change caused by carbon emissions has brought severe challenges to the sustainable development of global economy. In this context, this study constructs a weighted and directed carbon emission network for the European Union (EU). We use social network analysis to measure the indicators of the structural characteristics of the EU carbon emission network, and employ cluster analysis to investigate the role of countries in the carbon emission network. Furthermore, we use linear regression to explore the impacts of structural characteristics of carbon emission network on carbon emissions. The results show that, first the carbon emissions ties among the EU countries show a typical network structure during the sample period. Countries such as Germany, France, and Belgium are at the center of the carbon emission network, while Malta, Cyprus, and Croatia are at the edge. Second, different countries play the roles of "net spillover," "broker," "two-way spillover," and "net receiver" in the EU carbon emission network. Last, the increase of network density, the decrease of network hierarchy and the decrease of network efficiency all significantly reduce the carbon emission intensity of the EU, and narrow the spatial difference of carbon emissions among countries. Improving the weighted centrality indicators of nodes in the carbon emission network is helpful to reduce the carbon emission intensity of the EU countries. Based on the findings, this article puts forward policy suggestions for the collaborative governance of EU carbon emission abatement.